Mexico City is very large and much of what you want is far apart, so four days is the honest minimum. Three works if you drop the day trip.
The other constraint is altitude — 2,240 metres — which flattens people on the first day. Plan day one lightly.
Day one: the Centro Histórico
Deliberately gentle, because you have just arrived at altitude.
Morning. The Zócalo and the Metropolitan Cathedral, then the Templo Mayor at the corner of it — the Aztec temple found by electricity workers in 1978. Site first, museum second.
Midday. The Palacio Nacional for the Rivera murals, if it is open — check first, access changes.
Afternoon. Walk west to Bellas Artes for the Rivera, Orozco and Siqueiros murals, then up the Torre Latinoamericana or across to the Sears café for the view of it.
Evening. Tacos, and an early night.
Day two: Chapultepec
Morning. The Museo Nacional de Antropología, which is the reason to come to Mexico City at all. Four to five hours, ground floor only, and do not try to add the ethnography.
Afternoon. Either the Castillo on the hill — Maximilian’s apartments and the view down Reforma — or the park itself.
Note the park is closed on Mondays, museums included.
Evening. Roma or Condesa for dinner. This is where the eating is.
Day three: the south
Morning. Coyoacán — the plazas, the market tostadas, and the Casa Azul, booked online days in advance because walk-ups do not work.
Afternoon. Xochimilco and a trajinera on the canals. Weekday for the quiet version, Sunday for the party.
Or, if canals do not appeal: Casa Luis Barragán, booked weeks ahead, which is the best building in the city.
Evening. Lucha libre at Arena México if it is a Tuesday, Friday or Sunday.
Day four: Teotihuacán
The pyramids, an hour north by bus from Terminal del Norte. Go early — the site opens at nine and there is no shade.
Back in the afternoon for Mercado de San Juan or the Museo de Arte Popular.
What to book ahead
Frida Kahlo — days ahead, timed. Casa Luis Barragán — weeks ahead. Pujol or Rosetta if you want them — weeks. Everything else is turn-up.
Two closures to plan around
Mondays: Chapultepec park and nearly every museum in the city.
Palacio Nacional: access has been changed, restricted and suspended repeatedly. Check before crossing the Zócalo for it.
When to come
October to April is the dry season and the better half of the year — sunny days, cool nights, and the air at its clearest in autumn.
February to May is the warmest and also when air quality is at its worst, with pollution episodes trapped in the valley.
June to September is the rainy season, which in practice means brilliant mornings and a heavy downpour in the late afternoon. It is the low season, it is green, and the rain is easy to plan around — be indoors at five.
Late October into early November is Day of the Dead and is now the peak: book months ahead.
The altitude, restated
At 2,240 metres the first day is harder than you expect. The itinerary above deliberately starts with the flat Centro rather than a pyramid or a hill.
Drink more water than usual and go carefully on alcohol the first evening. See altitude and safety.
Three days, if that is all you have
Drop Teotihuacán. It is the thing most people would rather not lose, so the alternative is to drop the southern day and do Coyoacán and Xochimilco on a return visit — the pyramids are harder to substitute.
Getting oriented
The city is enormous but the visitor’s part is not. The Centro Histórico is in the middle; Reforma runs diagonally north-east to south-west from it through Juárez to Chapultepec; Roma and Condesa sit just south of Reforma; Coyoacán and San Ángel are ten kilometres further south.
Almost everything above is within that band.
What to skip
The Torre Latinoamericana and the Sears café — do one, they are the same view.
Organised Teotihuacán tours that bundle a shopping stop and the Basilica; the bus is an hour and costs almost nothing.
The replica Island of the Dolls at Xochimilco, sold as the real one, which is two hours further out.
If it rains
In the rainy season it will, in the late afternoon, heavily and briefly.
The Anthropology Museum, the Templo Mayor museum, Bellas Artes and the Museo de Arte Popular will absorb an afternoon each. The Centro’s arcades and the covered markets work too.
Streets flood quickly and drainage struggles; a downpour can make a fifteen-minute walk impassable for half an hour.