The Museo Nacional de Antropología
If you see one thing, see this. Purpose-built in Chapultepec Park around a vast central courtyard and its cantilevered fountain, it holds the Aztec Sun Stone, monumental Olmec heads and hall after hall of pre-Hispanic civilisations. Budget half a day and accept that you will not finish it.
A historic centre with real weight
The Zócalo is one of the largest city squares anywhere, flanked by the Metropolitan Cathedral and the excavated Templo Mayor, the Mexica ruins found under the colonial street grid in the 1970s. A few blocks away, the Palacio de Bellas Artes pairs a marble art nouveau exterior with an art deco interior, murals by Mexico's giants, and a Tiffany glass stage curtain.
Neighbourhoods you actually want to live in
Roma and Condesa are the reason first-timers extend their stay: early twentieth-century apartment blocks, jacaranda-lined streets, roundabout parks and a cafe on every corner. Coyoacan, further south, is a village-scaled colonial quarter and home to the Frida Kahlo Museum in the Casa Azul, which typically sells out well in advance online.
The big excursions
Teotihuacan, with the Pyramids of the Sun and Moon, is an easy day trip northeast. Xochimilco's canals and painted trajineras are a UNESCO-listed remnant of the lake system the city was built on.
March to May is warm and dry. The rains arrive around May and run to October, usually as an intense late-afternoon downpour rather than an all-day grey. Late October into early November brings Day of the Dead, when the city is spectacular and accommodation is at its tightest.