Mexico City

One of the greatest museums in the world — a sweeping, beautifully designed journey through Mexico's ancient civilisations, from the colossal Olmec heads to the Aztec Sun Stone and a full-scale Maya tomb, in Chapultepec park. Overwhelming in the best way; give it half a day, and don't miss the Aztec hall.

La Casa Azul — the cobalt-blue Coyoacán house where Frida Kahlo was born, lived, painted and died, kept as she left it, full of her art, clothes, wheelchair and spirit. Intimate and deeply moving, the highlight of any art-lover's trip; book a timed ticket online well ahead, as it always sells out.

One of the largest squares in the world, the vast ceremonial heart of the city and nation — flanked by the huge Metropolitan Cathedral and the National Palace, on the site of the Aztec capital's sacred centre. Come for the sheer scale, the flag-lowering ceremony, and the Aztec dancers on the flagstones.

One of the biggest city parks in the Americas — lakes, woods, a zoo and a clutch of great museums, crowned by the hilltop Chapultepec Castle, the only royal castle in North America, with sweeping views down Reforma. The city's green lungs; come Sunday when all of Mexico City is out enjoying it.

Mexico City may be the best street-food city on earth, and the taco al pastor is its king — marinated pork shaved off a spit onto a warm tortilla with pineapple, coriander and salsa, for a euro or less. Eat standing at a taquería where the queue is longest; then work through quesadillas, tlacoyos and elote.

The excavated ruins of the Aztecs' great double pyramid, unearthed right beside the cathedral — the sacred heart of Tenochtitlan, over which the Spanish built their city. Walk the raised paths through the layers, then see the astonishing carved stone deities and offerings in the superb attached museum.

The city's dazzling white-marble arts palace — an Art Nouveau and Art Deco masterpiece topped with a stained-glass Tiffany curtain, its interior lined with epic murals by Rivera, Orozco and Siqueiros. Catch the Ballet Folklórico dance show, or just admire it, best from the café terrace of the Sears building opposite.

Board a trajinera — a wide, brightly painted flat boat poled through the last of the Aztec canals in the city's south, past floating gardens, with mariachi boats and food vendors pulling alongside. A joyous, boozy, only-here fiesta on the water, especially with a group; go on a weekend for the full party.

Inside the National Palace on the Zócalo, Diego Rivera's vast, breathtaking staircase murals tell the entire sweep of Mexican history, from Aztec myth to revolution — one of the world's great works of public art, and free. Bring ID to enter; a powerful, unmissable hour with the nation's story on the walls.

A gloriously theatrical night at the wrestling — masked luchadores in dazzling costumes flying off the ropes to a roaring, family crowd at the Arena México, part sport, part pantomime, all spectacle. Cheap, hilarious and pure Mexico; grab a beer, a mask and a ringside seat and join in the chants.

The cobbled colonial heart of Coyoacán — twin leafy plazas with a fountain and a church, weekend craft stalls, mariachis, and a wonderful covered market where you eat tostadas piled high and drink fresh aguas frescas. The city's most charming, village-like afternoon; pair it with the Frida house nearby.

A shimmering, silver-tiled, curvaceous landmark building in Polanco housing a magnate's huge free art collection — a lot of Rodin sculpture, plus European masters and Mexican art, over six spiralling floors. As much about the extraordinary architecture as the art; free, and next to the Jumex contemporary museum.

The city's most delightful barrios for a wander — tree-lined streets of art-deco and beaux-arts villas, leafy parks like Parque México, independent bookshops, third-wave cafés and design shops. Do nothing in particular: stroll, brunch, browse, and feel why everyone wants to live here.

The city's grand, tree-lined boulevard, modelled on the Champs-Élysées, sweeping past monuments and skyscrapers to the golden Angel of Independence, its symbol. Walk or cycle it (it's car-free on Sunday mornings), pausing at the roundabout statues; the ceremonial spine of modern Mexico City.

Drink like a chilango — smoky mezcal or tequila sipped neat in an old-school cantina or a hip Roma mezcalería, with botanas (snacks) to share. From century-old wood-panelled bars to rooftop cocktails, the city's nightlife is deep and brilliant; start with a mezcal flight and let the night unfold.