There is a reason Barcelona consistently ranks as one of Europe's most visited cities and one of the best cities in Spain to visit in any year, any season, any age. It is the only major city on earth where you can spend a morning at a beach, an afternoon inside a UNESCO World Heritage basilica that has been under construction for 143 years, and an evening in one of the world's great restaurant neighbourhoods — all without touching a car. The city is built for walking and for looking, and it rewards both with a generosity that few urban places manage.

Antoni Gaudí is the reason most people put Barcelona on their list, and rightly so. The Sagrada Família is the most extraordinary building currently under construction on the planet — a cathedral that simultaneously references Gothic architecture, organic natural forms, and a visual language so personal it has no equivalent anywhere else. La Pedrera (Casa Milà), Casa Batlló and Park Güell complete the essential Gaudí circuit, but do not make the mistake of spending all your Barcelona time inside monuments. The Gothic Quarter (Barri Gòtic) is the city's oldest neighbourhood and one of the best urban labyrinths in Europe — narrow medieval streets that open unexpectedly onto Roman ruins, baroque churches and hidden squares where cats sit in the sun and nobody is in a hurry.

The food in Barcelona operates in parallel to the architecture: both are taken very seriously, both have been influenced by a specific Catalan cultural identity that is distinct from the rest of Spain, and both reward the visitor who seeks out the local rather than the tourist version. The Mercat de la Boqueria on La Rambla is too crowded and too expensive — the locals go to the Mercat de Santa Caterina in El Born, a spectacular mosaic-roofed market with genuinely good produce and genuinely local prices. For dinner, El Eixample offers the highest concentration of excellent Catalan restaurants in the city.

Madrid is the city that takes a day to like and a lifetime to love. Where Barcelona announces its qualities immediately — the architecture, the light, the sea — Madrid keeps them slightly hidden, behind a facade of official-looking avenues and government buildings that gives no indication of the extraordinary cultural life taking place inside them. Push through the official exterior and what you find is one of the most intellectually stimulating, socially generous and aesthetically rewarding cities in Europe.

The three great museums of the Paseo del Prado — the Prado itself, the Reina Sofía and the Thyssen-Bornemisza — form the most concentrated collection of world-class art in any comparable urban area. The Prado alone contains the greatest collection of Spanish painting on earth (Velázquez, Goya, El Greco) and one of the finest collections of Flemish painting outside the Low Countries. Goya's Black Paintings, transferred from the walls of the Quinta del Sordo to the Prado in the 1870s, are among the most psychologically disturbing works in the history of Western art and are housed in a room that most visitors walk through without fully understanding what they are looking at. Look slowly.

Madrid is also the best city in Spain for food in the broadest sense — not the most distinguished gastronomically (that is San Sebastián) but the most generous and varied. The Mercado de San Miguél, the tapas bars of La Latina, the chocolaterías of Madrid Antiguo that serve churros con chocolate at 3am to people who have just left the clubs of Malasaña — Madrid's food culture operates without reference to the clock in a way that feels simultaneously chaotic and entirely logical. The city stays up late not because it is trying to, but because the food is better at midnight than at seven.

Seville is the city where Spain is most fully itself. Where Madrid is the capital and Barcelona is the international brand, Seville is the beating emotional heart of a culture that has been making art, music and architecture of extraordinary quality for three thousand years. The city is smaller than it sounds (population 700,000 — the fourth-largest in Spain), more walkable than you expect, and more beautiful per square metre than almost anywhere in Europe. The historic centre takes perhaps forty minutes to cross on foot and contains five UNESCO World Heritage monuments.

The Real Alcázar is the most underrated palace complex in Europe — a royal residence still in use today that layers Moorish mudeíjar architecture, Gothic fortification and Renaissance expansion into a building that reads as a complete architectural history of the Iberian Peninsula from the 10th century to the present. The Patio de las Doncellas, the Salón de Embajadores and the gardens — 15 acres of fountains, hedgerows, peacocks and orange trees — constitute the single most beautiful domestic space in Spain. The Catedral de Sevilla, built on the site of the Great Mosque of Seville, is the largest Gothic cathedral in the world and contains the tomb of Christopher Columbus.

Flamenco in Seville is not a tourist attraction — it is a living cultural practice that has been performed in the city's tablãos, neighbourhood bars and private houses for generations. The Triana neighbourhood, across the Guadalquivir from the historic centre, is the traditional home of Sevillian flamenco and still home to its best practitioners. An evening of flamenco in a small Triana venue, with a glass of manzanilla sherry and a plate of prawns from the nearby port of Sanlúcar, is one of the most complete sensory experiences that Spain makes available to the visitor.

San Sebastián (Donostia in Basque) is the most extraordinary food city in Europe per capita, an argument that can be sustained empirically: it has more Michelin stars per square kilometre than any city on earth except Kyoto. But this number misses the more remarkable thing about the city's food culture, which is that the highest quality cooking is not concentrated in expensive restaurants but distributed across hundreds of pintxos bars in the old town (Parte Vieja), where masterfully prepared food — tortilla al estilo de Betàm, foie gras on toast with quince, kokotxas al pil-pil — is served for €2-3 per piece to standing customers who move from bar to bar in a specific social ritual that has no equivalent anywhere else in the world.

This would be enough. But San Sebastián also has one of the most beautiful beaches in Europe: the Playa de La Concha, a perfectly curved bay enclosed by Monte Urgull on one side and Monte Igueldo on the other, with promenade architecture so elegant that it read as the most sophisticated seaside resort in Europe at the turn of the 20th century and still does. The town is compact enough to walk everywhere, the Basque people are exceptionally hospitable to visitors who make any effort to appreciate their culture, and the combination of mountain, ocean and urban sophistication gives the city an environmental quality that is genuinely exceptional.

For the food-focused visitor: Arzak, Mugaritz and Akelarre represent the summit of Basque haute cuisine, but you will eat as well at any of the pintxos bars in the old town for a fraction of the cost and with a quality of social experience — standing at a zinc bar with strangers, passing plates between you, arguing about which version of the tortilla is better — that no tasting menu can replicate.

Bilbao is the city that proves urban regeneration can be beautiful. In the 1980s it was a declining industrial port — steel mills, shipyards, the Nervión river the colour of rust. The Guggenheim Museum Bilbao, which opened in 1997 to the designs of Frank Gehry, changed everything. Not metaphorically — literally. The museum's arrival triggered a complete transformation of the city's waterfront, economy and international reputation, and the process known as the "Bilbao Effect" has been studied by urban planners in every major city on earth as evidence that architecture of sufficient quality can change the fortunes of a post-industrial city.

The Guggenheim itself — titanium curves catching Basque light and reflecting the river, Jeff Koons's giant floral puppy at the entrance, Louise Bourgeois's spider Maman guarding the waterfront steps — is simultaneously a great building and a great piece of conceptual art. Its permanent collection includes some of the most important works of late 20th-century art, and its temporary exhibitions are consistently among the best in Europe. But the building is the exhibit: Gehry created a structure that is as significant as anything inside it.

Beyond the Guggenheim, Bilbao offers the Casco Viejo (old town) — seven streets known as the Siete Calles, full of pintxos bars that rival anything in San Sebastián — and the Mercado de la Ribera, the largest covered food market in Europe, which has been completely renovated and now combines serious gastronomy with an extraordinary setting on the riverfront. The combination of contemporary architecture, Basque food culture and a city that has visibly remade itself from industrial grime to European destination makes Bilbao one of the most intellectually stimulating city breaks available from the UK.

Valencia is Spain's best-kept secret from British visitors, a city of 800,000 on the Costa del Azahar that combines a historic medieval centre, an extraordinary piece of futurist architecture, 12km of urban beach, and the original, authentic home of paella valenciana — the dish that most of the world has been making incorrectly for sixty years (it contains chicken, rabbit and green beans, not seafood; rice cooked in a flat pan, not risotto-style; a socarrat — a crisped bottom layer — not a uniformly wet texture).

The Citat de les Arts i les Ciències (City of Arts and Sciences), designed by Santiago Calatrava and Félix Candela, is the most extraordinary piece of contemporary architecture in Spain outside the Guggenheim Bilbao. The complex — white concrete and blue pool water, the forms of bones and shells translated into civic buildings — is a museum complex, planetarium, opera house and aquarium simultaneously, and it occupies the former course of the Turia river that was diverted after the catastrophic 1957 floods. The riverbed itself became a 12-kilometre linear park that is one of the great urban planning achievements of 20th-century Europe.

The Mercat Central of Valencia, completed in 1928, is the most beautiful food market in Spain — a Modernista building of iron, glass and ceramics that houses a daily market of extraordinary quality. The fresh produce, the salt cod, the tiger nuts (chufa) for authentic horchata, the eels from the Albufera lagoon for the authentic local variant of paella — everything is here. Valencia in March, during the Las Fallas festival — huge papier-mâché sculptures built over months and burned in one night to the accompaniment of spectacular fireworks — is one of the most extraordinary cultural events in Europe and the best single reason to choose Valencia over any other Spanish city for a March visit.

Málaga has completed one of the most successful urban transformations of any Spanish city over the past twenty years, transitioning from a beach-resort gateway (most visitors saw it only through the windows of an airport transfer) to a genuine cultural destination with an extraordinary density of world-class museums, a completely revived historic centre, and a food scene that is among the best in Andalucía. The key to understanding modern Málaga is the Soho district — the former port area that has been comprehensively regenerated as a street art and gallery district, and the Muelle Uno waterfront development — combined with the fact that the city has more museums per square kilometre than any other Spanish city.

The Museo Picasso Málaga occupies the 16th-century Buenavista Palace and contains 233 works donated and loaned by Picasso's heirs. It is not the most comprehensive Picasso collection in the world (that remains in Paris) but it is the most intimate, in the city where he was born and which informed his earliest artistic education. The Casa Natal (birthplace) is a short walk from the museum and provides a complementary perspective on the artist's earliest formation. The Centre Pompidou Málaga — a satellite of the Paris institution — brings French contemporary art to the Mediterranean in a remarkable cube of coloured glass panels on the waterfront.

Eating in Málaga is eating in the present tense of Andalusian food culture. The city's boqueron (fresh anchovy), espeto de sardinas (sardines grilled on bamboo poles over wood fires directly on the beach), and fritura malagueña (mixed fried seafood) are dishes with no equivalent anywhere else in Spain, prepared to standards that the tourist-focused Costa del Sol has historically failed to maintain but that the revived city centre consistently achieves.

Cádiz is one of the oldest continuously inhabited cities in Western Europe — founded by Phoenician traders around 1100 BC — and it sits on a narrow peninsula in the Atlantic with the sea visible from almost every point in the historic centre. This geographical isolation has given the city a specific character that is unlike any other Andalusian city: more African in quality of light, more Atlantic in temperament, more aware of itself as a place that exists at the edge of the known world. The city that launched Columbus's second and fourth voyages. The city that gave Spain the first liberal constitution in 1812. The city that still understands itself as exceptional.

The food culture of Cádiz is built on the Atlantic: tortillita de camarones (shrimp fritters so thin they are more lace than fritter), chipirones (tiny squid, fried whole), ortiguillas (sea anemones, battered and fried — extraordinary and unavailable anywhere else in Spain), all served with a glass of manzanilla from the nearby port of Sanlúcar de Barrameda. The combination of sherry wine culture and Atlantic seafood is the most distinctive and underrated food culture in Spain.

The Gaditano Carnaval — held in February, the most elaborate and satirical street carnival in Spain — is the best-kept secret of Spanish festivals. The chirigotas (comic singing groups) and comparsas (more serious groups) write entirely new material every year specifically targeted at the political events of the preceding twelve months, and perform it in the streets and the Gran Teatro Falla in a combination of satire, musical invention and collective joy that defines the specific cultural genius of Cádiz.

Palma de Mallorca is what happens when you take one of the most naturally beautiful Mediterranean settings on earth — a bay of remarkable turquoise water enclosed by mountains on one side and the open sea on the other — and build on it, without catastrophic failure, for two thousand years. The result is a city of considerable architectural distinction (the Gothic Catedral de La Seu, one of the great medieval buildings of the Mediterranean; the Castell de Bellver, a perfectly circular Gothic castle that functions as the city's landmark; the Palau de l'Almudaina, a Moorish royal palace still used by the Spanish royal family) inside a landscape of corresponding natural distinction.

Mallorca as a whole is larger and more varied than most British visitors expect: the Serra de Tramuntana mountain range running along the northwest coast is a UNESCO World Heritage landscape of olive groves, limestone cliffs and mountain villages (Deià, Sóller, Valldemossa) where Chopin composed and George Sand complained about the weather. The east coast — the Llevant — contains some of the most beautiful coves in the Mediterranean, accessible by boat from the beach resort towns that line this coast. The interior — Es Pla — is a landscape of cereal fields, almond orchards and wine country (the Binissalem DO produces some of the most interesting red wines in Spain from the indigenous Manto Negro grape) entirely unknown to the package-holiday visitor.

Palma's food scene has transformed dramatically in the past decade: the old town now contains some of the most serious restaurants in Spain, concentrated around the Mercat de l'Olivar and the streets of the Born quarter. A meal at one of the Born's terrace restaurants, with Mallorcan lamb, sobrassada (paprika-cured pork sausage) and the local Macabeu white wine, is the complete Mallorcan evening.

Córdoba was, in the 10th century, the largest and most sophisticated city in Western Europe — a capital of learning, tolerance and architectural ambition under the Umayyad Caliphate that simultaneously housed the world's largest library, produced advances in mathematics, medicine and astronomy that would not reach the rest of Europe for two centuries, and built the monument that remains the most visited site in Andalucía: the Mezquita-Catedral.

The Mezquita is one of the strangest and most powerful buildings in the world. It was built as the Great Mosque of Córdoba beginning in 785 CE, expanded over the next two centuries to accommodate the growing population of a city then exceeding 500,000 inhabitants, and then — after the Christian Reconquest of 1236 — a Gothic cathedral was built directly inside it, inserting a 16th-century Christian church into the heart of an 8th-century mosque in a single act of architectural superimposition that is simultaneously barbaric and accidentally extraordinary. The result — the infinite forest of 856 red-and-white striped arches, interrupted by the Renaissance nave and chancel of the cathedral — is unlike anything else on earth. Even Carlos V, who commissioned the insertion, reportedly regretted it: "You have destroyed something unique to build something ordinary."

The city around the Mezquita is equally extraordinary in May, when the Festival de los Patios opens the private courtyards of Córdoba's historic houses to the public. These flower-filled patios — jasmine, geraniums, plumbago — are a UNESCO Intangible Cultural Heritage and the most beautiful horticultural display in Spain, competing for prizes that the neighbourhood families take with a seriousness verging on aggression. The combination of La Mezquita, the Jewish Quarter (Judería), the Medina Azahara (the vast Umayyad palace-city three kilometres outside the current city) and the patio culture makes Córdoba one of the most historically dense places in Europe.

Alicante is the Spanish city that British visitors have been underrating for forty years. As the hub of the Costa Blanca package-holiday industry, it has been consistently associated with an undiscriminating mass-market tourism that bears no relationship to the actual character of the city — which is one of the most historically interesting, architecturally coherent and gastronomically serious provincial capitals in Spain.

The Castillo de Santa Bárbara, rising on a sheer limestone outcrop 166 metres above the city and accessible via a lift cut directly through the rock, is a 9th-century Moorish fortress later expanded by the Spanish crown and offering what is arguably the finest panoramic view of any Spanish coastal city. Below it, the white-marbled Explanada de España — three million marble tiles in a wave pattern, palms, restaurants, the port — is one of the most civilised promenades in Mediterranean Spain.

The old town (El Barrio), climbing the hill behind the cathedral, is the neighbourhood where Alicante's genuine character lives: narrow streets, local bars, the Mercado Central (a Modernista market building of extraordinary quality), and the specific tapa culture of the Valencian interior that moves through the market's raw materials — local rice, vegetables from the Vega Baja, fish from the Albufereta — in ways that the beachfront restaurants never bother with. Alicante's rice dishes — arròs amb fesols i naps (rice with beans and turnips), the local arroz negro and the specific variant of paella called arròs en crosta (oven-baked rice with a pastry crust) — are as significant as any in Spain.

The largest of the Canary Islands, Tenerife occupies an anomalous position in Spanish tourism: simultaneously the most visited destination in all of Spain (over 16 million tourists annually) and the most underrated as a destination for independent travellers. The northern resorts — Puerto de la Cruz, the wine country of Orotava, the UNESCO World Heritage historic centre of La Laguna — bear no relationship to the package-resort south, and Mount Teide, the highest mountain in Spain at 3,718 metres and one of the largest volcanoes on earth by volume, dominates the island's centre with a presence that makes it impossible to mistake Tenerife for a flat island surrounded by beaches.

Teide National Park — the most visited national park in Europe and a UNESCO World Heritage site — is a landscape of lunar strangeness: the crater of a volcano surrounded by solidified lava fields in black, red and ochre, with the snow-capped summit visible from Morocco on clear days. The cable car to 3,555m provides access to a high-altitude landscape of extraordinary atmospheric clarity, and the permit-controlled summit itself (advance booking essential) offers the experience of standing inside the volcanic crater of a mountain that last erupted in 1909 and retains its geological drama intact.

Santa Cruz de Tenerife itself — the island's capital — is a serious city with excellent museums (the Museo de la Naturaleza y el Hombre, home to the world's most complete collection of Guanche mummies, is one of the most extraordinary archaeological collections in Spain), a genuine restaurant culture built on Canarian specialities (papas arrugadas with mojo picon, fresh fish from the Atlantic, the specific local variants of Canarian cuisine that have no equivalent on the mainland), and the Santa Cruz Carnival — second only to Rio de Janeiro in size and ambition, a fact that surprises every visitor who has come to Tenerife expecting beach restaurants.