Rio de Janeiro is the most visually spectacular city in the Western Hemisphere — a city in which the human drama is played out against a backdrop of such extraordinary natural scenery (the granite plugs of Sugarloaf and the Corcovado rising from the rainforest, the curve of Copacabana bay, the deep blue of Guanabara) that even the most prosaic daily activity acquires a theatrical quality. No other major city on earth offers the combination of Atlantic beaches, rainforest-covered mountains and urban density within the same city limits, and the specific quality of Rio's light — the subtropical shimmer of the bay, the way the golden late afternoon falls on the favela houses on the hillsides — makes it the most photographed city in South America.

The Cristo Redentor (Christ the Redeemer, Paul Landowski and Heitor da Silva Costa, 1931) — the 30-metre Art Deco statue of Christ atop the 710-metre peak of the Corcovado, arms outstretched over the city, visible from most of Rio on clear days — is the most iconic image in South America and the most complete expression of a city's relationship with its landscape. The ascent by rack railway through the Tijuca Forest (the world's largest urban tropical rainforest) is as extraordinary as the view from the summit: the Floresta da Tijuca covers 32 square kilometres of the Carioca mountains and is an urban wilderness of waterfalls, howler monkeys and orchids entirely surrounded by the city.

Carnival — five days in February or March when Rio hosts the largest street party on earth — is a complete category of human experience. The Sambódromo (Oscar Niemeyer, 1984), a 700-metre purpose-built parade avenue with permanent grandstands, hosts the escolas de samba (samba schools) who present parade performances that take up to a year to construct: thousands of dancers in elaborate costumes, floats of extraordinary scale, drums maintaining the bateria rhythm that forms the sonic backbone of everything. Outside the sambódromo, the blocos (informal street parades) fill the entire city — the Banda de Ipanema, the Cordão do Bola Preta — with participants numbering in the millions. Carnival in Rio is the only event of its scale that remains genuinely participatory rather than merely spectacular.

Buenos Aires is the most European city outside Europe — a capital of 15 million people on the Río de la Plata that was built and governed by successive waves of Spanish, Italian, French, Jewish and Eastern European immigrants whose cultures combined in the specific Argentine synthesis: a city of grand Beaux Arts boulevards (the Avenida de Mayo, modelled on Paris's Rue de Rivoli) and conventillos (immigrant tenements), of the Teatro Colón (one of the five best opera houses in the world) and the asado (Argentine barbecue, consumed on weekends with the seriousness of a religious rite), of psychoanalysis (Buenos Aires has more psychoanalysts per capita than any other city on earth) and tango.

Tango — the specific music and dance form that emerged from the immigrant conventillos of La Boca and San Telmo in the 1880s — is the most complete expression of Buenos Aires's character: the combination of longing, irony, physical intimacy and formal precision that defines not just the dance but the Argentine relationship with emotion generally. The milongas (tango dance halls) of San Telmo and Boedo, where the dance is performed by locals rather than tourists, are among the most extraordinary social spaces in South America: an entire adult culture built around a form of physical communication that requires years of study and creates, in its best expression, a conversation between two bodies that has no equivalent elsewhere.

The Recoleta Cemetery — where Eva Perón is buried in the Duarte family vault, surrounded by the elaborate mausolea of Argentina's 19th and 20th-century elite — is the most theatrical necropolis in the world: a city of the dead with its own streets, architectural schools and symbolic competitions that constitutes one of the most complete records of Argentine history available in a single walkable space. The MALBA (Museo de Arte Latinoamericano de Buenos Aires) houses the finest collection of 20th-century Latin American art on the continent, including Frida Kahlo's Self-Portrait with Monkey and Parrot and Xul Solar's extraordinary dreamscapes. The Palermo neighbourhood — 70 blocks of restaurants, bars, galleries and parks — is the best single neighbourhood in South America for an afternoon and evening, and the most complete expression of the specific Buenos Aires gift for making pleasure feel serious.

São Paulo is the most important city in Latin America by almost every measure that matters: economic output (the metropolitan area's GDP exceeds that of Argentina), cultural production (the city hosts the São Paulo Biennial — the world's oldest and second largest art biennial — the São Paulo International Film Festival, and a restaurant density that has led chefs from around the world to declare it the best city on earth for eating), immigrant diversity (the largest Japanese diaspora outside Japan; the largest Italian diaspora outside Italy; Lebanese, Syrian, Korean, Chinese, Spanish and Portuguese communities each contributing their specific culinary tradition to a food culture of extraordinary variety), and the specific urban energy of a city that was, as recently as 1900, a provincial town of 240,000 people and is now the seventh-largest metropolitan area on earth.

The Pinacoteca do Estado — one of the oldest art museums in Brazil (1905), housed in a renovated factory building in Luz — contains the most important collection of 19th and 20th-century Brazilian art: Anita Malfatti's proto-Expressionist work, Tarsila do Amaral's Abaporu (the painting that launched Brazilian Modernism in 1928, now at the MALBA in Buenos Aires — but the Pinacoteca gives the full context), Victor Meirelles's First Mass in Brazil (1861). The Museu de Arte de São Paulo (MASP), Oscar Niemeyer's red concrete suspension building over the Avenida Paulista, houses the largest collection of Western art in the Southern Hemisphere — El Greco, Rembrandt, Renoir, Van Gogh, Picasso — displayed on transparent crystal easels in a system designed by Pietro Maria Bardi to show both sides of every canvas.

The food culture of São Paulo is the most complex in Latin America and among the most complex in the world. The Japanese influence — from the Liberdade neighbourhood, the centre of the largest Japanese community outside Japan — produced the specific São Paulo sushi tradition that is different from Japanese sushi (larger, more Brazilian, with local fish) and has been exported to the rest of Brazil. The Lebanese and Syrian communities of the Bixiga and Higienópolis neighbourhoods produced a Middle Eastern-Brazilian fusion cuisine that is entirely specific to São Paulo. And the padaria culture — the neighbourhood bakeries that are the social centres of every São Paulo bairro, open from 6am to midnight, serving coffee and pão de queijo (Brazilian cheese bread) to three generations of the same families simultaneously — is the most democratically distributed quality food culture in any major South American city.

Havana is the most intact colonial city in the Caribbean — a city of 2.1 million people where the 16th, 17th, 18th and 19th centuries are visibly present in the architecture of the Old Havana (Habana Vieja), a UNESCO World Heritage site of extraordinary density: the four original colonial plazas (Plaza de Armas, Plaza Vieja, Plaza de San Francisco de Asís, Plaza de la Catedral) each with their own architectural ensemble, connected by streets of Baroque and Neoclassical buildings whose painted facades — turquoise, ochre, salmon, yellow — are peeling in the specific way that makes the city simultaneously decrepit and beautiful. The specific aesthetic quality of Havana — the combination of colonial grandeur and infrastructural decay, of the Malecón seafront's crashing Atlantic waves and the vintage American cars from the 1950s that serve as taxis — is unlike anything else in the Americas.

The music culture of Havana is the most concentrated in the Caribbean: the son cubano tradition (the synthesis of Spanish guitar and African drumming that produced salsa, mambo, cha-cha-cha and rumba), the trova tradition of singer-songwriters performing in bars and theatres, the jazz tradition centred on the Jazz Café and the Casa de la Música, and the son montuno bands performing in the courtyards of Old Havana's casas de cultura — all operating simultaneously in a city where music is the most consistent expression of public life. The EGREM recording studio, where the Buena Vista Social Club albums were recorded, is still operating and still producing musicians of international quality in the specific Cuban tradition.

Old Havana's restoration — begun in the 1980s under the direction of the City Historian Eusebio Leal Spengler and funded by tourist revenue — is the most ambitious historic city restoration programme in Latin America: 900 buildings restored or under restoration, the colonial fabric repaired, the plazas functioning again as civic spaces. The specific social character of Old Havana — its combination of restored monuments and still-inhabited colonial buildings, its population of Habaneros going about their daily lives in streets designed for horses and carriages — makes it the most complete urban time capsule in the Americas, and the most photographed city in the Caribbean.

Rosario is the city that produced, within a generation, the two most transformative Argentines of the 20th century: Ernesto "Che" Guevara (born Rosario, 1928) and Lionel Messi (born Rosario, 1987). This coincidence of birthplace is either a remarkable accident or a function of something specific in the city's character — its independence from Buenos Aires's cultural dominance, its tradition of radical politics (it was a centre of anarchist and socialist labour movements in the early 20th century), its specific relationship with the Paraná river and the agricultural interior of the Argentine pampas.

The Monumento a la Bandera (Monument to the Flag, Ángel Guido and Alejandro Bustillo, completed 1957) — the massive Rationalist monument on the Paraná waterfront where General Belgrano first raised the Argentine national flag in 1812 — is the civic centrepiece of Rosario and one of the most architecturally ambitious public monuments in Argentina: a propylaeum, a triumphal arch, a bas-relief frieze and a 70-metre tower containing an eternal flame, all in local travertine, set against the broad expanse of the Paraná river. The riverside promenade — 10km of regenerated waterfront from the Costanera Sur to the Parque Urquiza — is the finest urban riverside development in Argentina and the best place in the city for the specific Rosarino pleasure of watching the Paraná's brown water move past at 4pm while drinking mate.

The Messi sculpture in the museum bearing his name in his childhood neighbourhood of Las Heras is the obvious pilgrimage point, but the more interesting address for the football lover is the Estadio Gigante de Arroyito (Newell's Old Boys stadium, where Messi played his first youth football) and the Estadio Marcelo Bielsa (Rosario Central, the rival club, named after the coach who transformed Argentine football in the 1990s). The specific Rosarino passion of the clásico between Newell's and Central — a derby of the two city clubs that divides families, streets and workplaces — is the most intense local football rivalry in Argentina, which is to say one of the most intense in the world.