Mexico City

A square more than 200m on a side, with the cathedral and the national palace taking two of its faces. Soldiers raise an oversized flag each morning and fold it down again at dusk.

Electrical work in 1978 uncovered this Aztec temple beside the cathedral. The pyramid was rebuilt over itself seven times, so the layers sit inside one another.

Each hall takes one civilisation, dividing the Maya from the Aztec and from Oaxaca. In the courtyard an umbrella roof 82m across rests on a single column.

The blue house in which the painter was born and died, its kitchen and bedroom left as they were. Tickets sell online only and often go days ahead.

Farming channels from Aztec times survive, worked by painted flat boats pushed with a pole. Smaller craft carrying food and musicians pull alongside and name a price.

A castle on the hill, and the only one on this continent that a monarch actually lived in. A stained glass gallery and a roof garden open the city on every side.

A marble theatre that has sunk close to four metres under its own weight. Its stage curtain shows two volcanoes made from a million pieces of glass.

Cobbles and low houses survive from an older village now swallowed by the city. A weekend market fills its square, and the queue outside the ice cream shop runs long.

Masked wrestlers fight while the crowd shouts along with every move. Some arenas bar cameras, so it is checked at the door.

Sixteen thousand silver hexagonal tiles wrap a building climbed by a spiral ramp. No ticket is taken, and the Rodin sculptures are gathered on the top floor.

Begun in 1573 and only finished in 1813, the largest cathedral in the Americas. It stands on soft filled-in lakebed and is sinking unevenly. A pendulum hung mid-nave marks the lean against a scale on the floor.

A pair of houses in San Angel built by Juan O'Gorman in the early 1930s. The big red one was Diego Rivera's studio and the small blue one Frida Kahlo's, joined by a rooftop bridge. Crowds here are thin next to the Blue House in Coyoacan.

The central post office, finished in 1907 by Adamo Boari, who also designed Bellas Artes. The gilded iron staircase and glass ceiling are the draw, and the counters still run as a post office. Buy stamps and post a card from here as a keepsake.

An 18th-century noble mansion whose outer walls are covered entirely in Puebla tiles. The courtyard is now a Sanborns restaurant, so a cup of coffee gets you inside. On the stairwell wall is a mural Orozco painted in 1925.

Finished in 1956, this tower rises over the historic centre and rode out the big earthquakes of 1957 and 1985. The 44th-floor deck gazes almost vertically onto the domes of Bellas Artes. On clear mornings the volcanoes show in the distance.

One of the most visited Catholic shrines on earth. In the round new basilica of 1976, moving walkways run below and behind the altar, carrying people past the Virgin's image without stopping. Millions gather the night before its 12 December feast.

Hundreds of craft stalls from many states gathered beside Balderas metro station. Oaxacan textiles and Jalisco glassware sit a few aisles apart for comparing. Prices sit below the tourist-zone shops, and buying several pieces earns a discount.

Two neighbourhoods of Art Deco buildings and cafes under shady street trees. Parque Mexico in Condesa sits on a former racecourse, so Avenida Amsterdam around it still traces the oval of the old track. Walk one loop of it and you have seen both.

A public library opened in 2006, its steel stacks layered as if hanging in mid-air. A whale skeleton sculpture by Gabriel Orozco is suspended in the central hall. It sits right beside Buenavista station, and entry is free.

A museum built around a single mural, at the far western edge of the Alameda. Dream of a Sunday Afternoon in the Alameda, painted in 1947, runs more than 15m long. It was cut from its hotel and moved here after the 1985 earthquake wrecked the building.

Paseo de la Reforma, home of the Angel of Independence, shuts out traffic on Sunday mornings and is handed to cyclists and walkers. Rent an Ecobici from the docks around town and ride as far as Chapultepec Forest. Traffic returns in the afternoon.

Juan O'Gorman covered all four walls in mosaic made from coloured stone gathered across the country. UNESCO inscribed the whole university campus on its World Heritage list in 2007. Even during term, there is no restriction on viewing the walls from outside.

The square where mariachi bands in full suits wait for customers. They charge per song, so agree on a price before asking for one. A tequila and mezcal museum faces the plaza, and the band count grows as the night gets later.

Aztec market-city ruins, the Santiago church built from their stones, and modern tower blocks share one square, hence the name. Students protesting here were massacred on 2 October 1968, and a memorial stands in the plaza.