Rome does not compete with other European cities for the title of most historically significant. It simply holds it, without contest, by the weight of accumulated centuries. No other city on earth contains a continuous inhabited history of 2,800 years within its current city limits — the Roman Forum where senators argued, the Palatine Hill where Augustus lived, the Colosseum where 50,000 people watched gladiators, and the Sistine Chapel where Michelangelo painted the most scrutinised ceiling in the history of Western art are all accessible on foot in a single long afternoon. The difficulty of visiting Rome is not finding things to see; it is deciding what to leave out.

The essential Rome is concentrated in an area walkable in a single morning: the Piazza Navona (Bernini's Fountain of the Four Rivers, the elongated oval of a former chariot-racing stadium), the Pantheon (the most perfectly preserved ancient building on earth, its unreinforced concrete dome larger than that of St Peter's), the Campo de' Fiori (a morning flower market that becomes a drinking district by nightfall), and the Trastevere neighbourhood across the Tiber, where the medieval street pattern survives intact and the restaurants are the best value in the city. This is Rome before the Tourist Rome, the city that Romans actually live in.

The Vatican — technically a separate sovereign state — requires separate planning: the Vatican Museums and the Sistine Chapel should be booked online weeks in advance and visited on opening (they are quieter in the first forty minutes than at any other point in the day). The chapel itself is smaller than most visitors expect, and more overwhelming. The ceiling is not a flat surface but an architecture of painted figures in painted niches at painted heights — Michelangelo invented a complete three-dimensional architectural fiction and painted it as convincing illusion. Stand in the centre and look up slowly. The Last Judgement on the altar wall, painted twenty-four years after the ceiling, is a different register entirely: urgent, physical, frightening.

Florence made the Renaissance. Not as a metaphor — literally. The city of Florence in the 15th century was the wealthiest banking centre in Europe under the patronage of the Medici family, and it was Medici money, Medici taste and Medici ambition that commissioned the works that defined Western visual culture for the next five hundred years. Brunelleschi's dome — the largest masonry dome ever constructed, completed without scaffolding by a method that Brunelleschi refused to reveal to his competitors — is the first building of the Renaissance and still the most impressive engineering achievement in the history of construction. Donatello's David — the first free-standing nude male figure since antiquity — was commissioned by Cosimo de' Medici. Botticelli's Birth of Venus was commissioned by the Medici family. Michelangelo learned to sculpt in the Medici gardens.

The Uffizi Gallery is the most important collection of Renaissance painting in the world — not the largest (that title belongs to the Louvre) but the most concentrated: room after room of works that changed the history of art, each room more extraordinary than the last, until you arrive at Room 10-14 and encounter the Botticellis (Primavera and Birth of Venus) which are simultaneously the most technically accomplished and the most emotionally direct works in the building. The museum requires several visits to see properly; on a single visit, focus on the first fifteen rooms and the second floor corridor.

The Oltrarno neighbourhood — across the Arno from the tourist-saturated historic centre — is where Florence actually lives: the artisan workshops of Via dei Serragli, the bars of Piazza Santo Spirito (the most authentic piazza in Florence), the Boboli Gardens behind the Palazzo Pitti, and the view from the Piazzale Michelangelo at the top of the hill behind the city — the panorama that shows you Florence in one image: the Arno, the bridges, Brunelleschi's dome rising over a city of amber terracotta, the Tuscan hills beyond.

Venice is the most improbable city on earth: 117 islands connected by 400 bridges and 150 canals, with no wheeled vehicles of any kind, built on wooden piles driven into a lagoon by refugees from the Lombard invasions in the 5th century and continuously inhabited since. The specific genius of Venice is that it was built not despite the difficulty of the environment but in explicit conversation with it — a city that took the constraints of water, tide, limited land and uncertain foundations and turned them into the most extraordinary urban aesthetic in the world. Every palazzo along the Grand Canal is a response to the problem of building on water, and the solutions — the light-absorbing pink and ochre plaster, the pointed Gothic arches designed to distribute weight efficiently, the narrow *calli* and *campielli* designed to maximise useable space — are beautiful because they are correct.

St Mark's Basilica is the most Byzantine building in Western Europe — a cathedral that looks like Constantinople, built to house the stolen relics of St Mark that Venetian merchants smuggled out of Alexandria in 828 CE under a layer of pork fat (to deter inspection by Muslim customs officials). The mosaics covering 8,000 square metres of interior gold ground are the most complete Byzantine decorative programme outside Istanbul. The Palazzo Ducale (Doge's Palace), connected to the state prison by the Bridge of Sighs, is simultaneously the seat of a maritime empire and the most beautiful secular Gothic building in Europe. The view from the Campanile of St Mark's Square covers the lagoon, the Lido, the islands of Murano and Burano, and the Alps on clear days.

The Peggy Guggenheim Collection on the Grand Canal occupies the unfinished Palazzo Venier dei Leoni and contains Guggenheim's extraordinary personal collection of 20th-century art — Pollock, Picasso, Dalí, Kandinsky, Magritte, all in rooms that open directly onto the Grand Canal's terrace. It is the most elegantly situated art collection in Europe, and it is entirely unlike anything else in Venice, which makes it the most useful single counterpoint to the medieval and Renaissance city around it.

Milan is the least typical Italian city and the most European. Where Rome exists in conversation with ancient history and Florence with the Renaissance, Milan exists in conversation with the present — with fashion, finance, design, contemporary art and the specific energy of a northern Italian city that has been the industrial engine of Italian prosperity since the mid-19th century. It is less beautiful than Rome or Florence in the postcard sense, and more interesting in the sense that matters: a city of extraordinary private collections, genuinely excellent restaurants that nobody outside Italy writes about, and two of the most extraordinary cultural objects in Western civilisation.

Leonardo da Vinci's Last Supper — painted on the refectory wall of the Convent of Santa Maria delle Grazie between 1495 and 1498 — is the most studied image in the history of art and still the most surprising. The painting is not on canvas or panel but directly on the refectory wall in an experimental tempera technique that Leonardo devised and that began deteriorating almost immediately after completion. What survives — through centuries of restoration, Napoleon's troops using the room as a stable, and a direct hit by Allied bombing in 1943 that destroyed the rest of the building but left the wall standing — is fragmentary, damaged and utterly overwhelming: the moment at which Christ has just said *one of you will betray me* and thirteen people are responding simultaneously.

The Duomo di Milano — a Gothic cathedral 600 years in construction, with 3,400 external statues and a capacity of 40,000 people — is the largest Gothic structure in Italy and one of the strangest buildings in Europe: entirely unlike the French Gothic cathedrals it nominally descends from, it has developed its own visual language over six centuries of continuous building, the later additions sometimes responding to the earlier ones and sometimes simply ignoring them. The rooftop walk is one of the most extraordinary architectural experiences in Italy — you are among the forest of Gothic pinnacles and statues at close range, the Milanese plain extending flat to the Alps in every direction.

Naples is the city that divides visitors more decisively than anywhere else in Italy. Those who love it — and many do, passionately — describe it as the most alive city in Europe: chaotic, generous, visually overwhelming, gastronomically extraordinary, historically dense beyond any reasonable expectation. Those who struggle with it describe the traffic, the noise, the disorganisation, the aggressive venditori around the main tourist sites. Both descriptions are accurate. Naples is not a city that makes concessions to visitor comfort, and it is richer for it: this is the Italian city that has retained its specific character most completely, that has been least cleaned up for the visitor, and that therefore offers the most complete encounter with what southern Italian urban culture actually is.

The Museo Archeologico Nazionale di Napoli houses the finest collection of ancient Roman art in the world — not because Naples collected it but because it was excavated from Pompeii and Herculaneum, the two Roman cities buried by the eruption of Vesuvius in 79 CE and preserved in extraordinary detail by the volcanic ash. The Pompeii site itself — reachable by train in 35 minutes — is the most completely preserved ancient city on earth: the bakeries still have carbonised bread in the ovens, the graffiti on the walls is still legible, the body casts of the citizens caught by the pyroclastic surge are simultaneously archaeological documents and profoundly human objects.

The Spanish Quarter (Quartieri Spagnoli) is the neighbourhood where Naples is most fully itself: narrow streets between seven-storey buildings, laundry strung between windows, basso dwellings where single rooms open directly onto the street, shrines to Maradona and the Madonna on the same wall. The food here — fried pizza from a street kiosk, sfogliatella from a bar that has been making it since 1818, ragù napoletano that has been simmering since seven o'clock this morning — is the most honest expression of what Italian cooking means before it became Italian cuisine.

Bologna has three nicknames that together constitute its entire personality: La Dotta (the Learned — it hosts the oldest university in the Western world, founded 1088), La Grassa (the Fat — it produces more and better food per square kilometre than any other Italian city), and La Rossa (the Red — both for its beautiful terracotta architecture and its historic left-wing politics). The city is less visited than Rome or Florence or Venice, which means it is also less tourist-adjusted: the restaurants are priced for local budgets, the bars are used by students and professors rather than tour groups, and the extraordinary medieval arcade system — 40km of covered walkways connecting the entire historic centre — was built for the citizens rather than the visitors.

The food of Bologna and Emilia-Romagna is the foundation of what most of the world understands as Italian cooking. Tagliatelle al ragù — what the rest of the world calls spaghetti Bolognese, which Bolognesi consider a travesty — is the local pasta dish, and in Bologna it is made with fresh egg pasta, rolled to exactly the width of the Asinelli tower divided by ten thousand (a local joke that is also a genuine legend). Tortellini, filled with prosciutto, mortadella and Parmigiano, are served in brodo (beef broth) and almost nowhere else in the world. Mortadella — the specific large-diameter cooked sausage that bears no relationship to any product called bologna outside Italy — is served in thin slices with fresh bread and is one of the most delicious things in Italian food culture.

The Due Torri — the Asinelli and Garisenda towers, two medieval skyscrapers built by rival families as symbols of wealth and power in the 12th century — are the most striking urban monuments in northern Italy outside Venice, and the view from the top of the taller tower (the Asinelli, 97 metres, 498 steps) covers the entire Po plain to the Alps in the north and the Apennines in the south.

Turin is the most underrated major Italian city — a place that combines exceptional food, extraordinary Baroque architecture, world-class museums and the specific elegance of a royal capital (it was the first capital of united Italy, from 1861 to 1865) without any of the tourist infrastructure of Rome or Florence. The city is laid out on a Roman grid plan in a way that no other Italian city is, its broad boulevards lined with Baroque buildings and covered arcades, the Alps visible from every north-facing street on clear days, the Po river winding through parks that give the city its surprising greenness.

The Mole Antonelliana — the building that appears on the Italian two-cent coin — was begun as a synagogue in 1863 and repurposed as the city's symbolic monument, now housing the Museo Nazionale del Cinema, which is housed in its extraordinary dome interior in one of the most inventive museum designs in Europe. The Museo Egizio (Egyptian Museum) is the second most important collection of ancient Egyptian artefacts in the world after Cairo, and its holdings include objects of extraordinary rarity and quality collected by Italian archaeologists in the 19th century.

Turin's caffè culture is the most refined in Italy — the city claims to have invented the espresso, the bicerin (hot chocolate, espresso and cream layered in a small glass), and the cioccolata tradition that produced Gianduja (hazelnut chocolate) and eventually Nutella. The historic caffès of Turin — Caffè Fiorio on Via Po, Caffè Al Bicerin near the Santuario della Consolata — are among the most beautiful café interiors in the world. For food, the Piedmontese culinary tradition (truffles, tajarin pasta, the bagna càuda sauce, the Barolo and Barbaresco wines from the hills forty minutes south) is the one Italian regional cuisine that has been most consistently undervalued by international visitors.

Pisa has the misfortune of being simultaneously one of the most remarkable architectural sites in Italy and the most reduced to a single image: the photograph of tourists pretending to hold up the tower. The tower is worth seeing — and climbing — beyond any ironic context: an 8th-century Romanesque bell tower of considerable beauty that happens to be tilting 3.97 degrees off vertical due to inadequate foundations in soft subsoil, and has been tilting progressively since its second floor was completed in 1178. The tilt is visible from a distance but only becomes genuinely disorienting when you are inside it, climbing the spiral staircase that seems perfectly level on one side and severely inclined on the other.

The Piazza dei Miracoli (Square of Miracles) that surrounds the tower is a UNESCO World Heritage site containing four separate monumental buildings: the tower, the Duomo di Pisa (completed 1118, the most ambitious Romanesque cathedral in Italy), the Battistero (the largest baptistery in Italy, with extraordinary Gothic pulpit by Nicola Pisano), and the Camposanto (the monumental cemetery with Gothic marble arcades and, until World War II bombing destroyed most of them, extraordinary 14th-century frescoes). The combination on a single grassed piazza, all in white marble from the Apuan Alps, is one of the most concentrated architectural experiences in Italy.

Pisa works best as a morning or afternoon from Florence rather than an overnight stay — the city beyond the Piazza dei Miracoli is pleasant but not extraordinary. The train journey itself (1 hour, through the Arno valley) is one of the more beautiful short train journeys in Tuscany, and the combination of Florence and Pisa in a single day is the most common and most successful Tuscany itinerary for visitors based in Florence.

Genoa (La Superba — the Superb) is Italy's best-kept secret for British visitors: a medieval port city of extraordinary historical and architectural interest that receives a fraction of the attention given to its neighbours Florence and Milan, and rewards the visitor who finds it with a concentrated urban experience unlike anything else in Italy. The city was, in the 13th and 14th centuries, one of the most powerful maritime republics in the Mediterranean — richer than Venice for a period, with colonies from the Black Sea to the Atlantic — and it built with an ambition that the current relative obscurity does nothing to diminish.

The Caruggi — the medieval lane system of the historic centre — are the most extensive and most authentic surviving medieval urban fabric in Italy. The lanes run from the historic Porto Antico (the old harbour, now redeveloped by Renzo Piano as a public waterfront) up through the historic centre, so narrow in places that opposite windows almost touch. Within this labyrinth: the Cattedrale di San Lorenzo with its black-and-white striped Gothic facade, the extraordinary concentration of Baroque palaces on the Via Garibaldi (a UNESCO World Heritage site, a single street lined on both sides with Genoese palaces of the 16th century — the Strade Nuove), and the Palazzo Rosso and Palazzo Bianco, two of the finest provincial art collections in Italy.

The food of Genoa and Liguria is the most distinctive of any Italian region — and the most internationally imitated with the least acknowledgement. Pesto genovese originates here and is made nowhere else with the same quality: the Genoese basil (basilico genovese DOP) has a specific delicacy of flavour that basil from other regions does not possess, and the pesto made from it bears the same relationship to what is sold in supermarkets as Champagne bears to sparkling water. The focaccia genovese — dimpled, olive-oiled, slightly brinish from sea salt, served warm — is the best bread product in Italy. The Ligurian coast east of Genoa — the Cinque Terre — is accessible by train in 45 minutes and constitutes one of the most beautiful short coastal hikes in Europe.

Palermo is the most cosmopolitan city in the Mediterranean, a designation it has held intermittently for three thousand years. Founded by Phoenicians, colonised by Greeks, conquered by Romans, taken by Arabs in 831 CE, captured by Normans in 1072, ruled by the Holy Roman Empire, incorporated into the Kingdom of the Two Sicilies — Palermo has accumulated its history in layers of architecture that coexist without resolution, each culture building on and through the previous one in a city that looks like nowhere else on earth.

The Arab-Norman architectural tradition — the specific synthesis of Islamic, Byzantine and Norman styles that emerged under the 12th-century Norman kings of Sicily — produced buildings that have no equivalent anywhere in Europe. The Cappella Palatina, the private chapel of Roger II (completed 1143), combines a Latin basilica plan with Byzantine gold mosaics covering every surface and an Arabic stalactite ceiling of extraordinary complexity — three distinct architectural traditions in one room, each at the highest level of its craft. The La Martorana and the San Giovanni degli Eremiti (with its distinctive pink domes, now a museum) extend the Arab-Norman tradition across the city centre.

The food markets of Palermo — Ballarò, Vucciria and Capo — are the most complete surviving examples of the medieval Islamic market tradition in a European city. The Ballarò in particular operates from 7am with a density and energy that has more in common with a Moroccan souk than with anything in continental Italy: the vendors' calls, the display of fish caught that morning, the street food (pane ca' meusa — spleen sandwich; sfincione — thick Sicilian pizza with anchovy and onion; fried artichoke hearts; arancine in four varieties) consumed standing up at the stalls. This is southern Italian food culture at its most unmediated and most extraordinary.