Four days in Mérida: two great Maya cities from one hotel room

Everything on the first evening is on one square, which is the pleasure of arriving here rather than in a large city. Laurel trees, confidenciales (the double S-shaped stone seats made for courting couples), an ice cream cart, and buildings on all four sides that are each worth walking into.

The cathedral is the austere one, which is unusual in Mexico and is partly a Franciscan choice and partly the result of looting during the revolution. It was finished in 1599 out of the stones of the Maya temple that stood on the same spot, and it is usually described as the oldest cathedral on the American mainland.

Across the square is the house the conqueror of Yucatán built for himself in 1549. Look up at the doorway: two Spanish soldiers in armour, each standing on the head of a Maya. It is the most explicit piece of political sculpture in the country and it has been there for nearly five hundred years.

Uxmal is an hour south on a good road and takes half the day. It is a quieter site than the famous one east of the city and a considerably more beautiful one: the Puuc style is all long horizontal facades covered in geometric mosaic, assembled from thousands of cut stones without mortar.

The first thing you meet is the great rounded pyramid, thirty five metres of it, with sides that slope in a curve nothing else in the Maya world does. Legend says a dwarf magician built it in a single night. Archaeologists count five separate rebuildings, which is less romantic and took rather longer.

Behind it the site opens out into courtyards and platforms. The long palace on the southern terrace is the masterpiece, a facade of some twenty thousand cut stones with the hooked nose of the rain god repeated along it in stacks, because in this part of Yucatán there are no rivers and everything depended on rain.

Leave at seven. The drive east takes a little under two hours and the gates open at eight, and the first hour is the only one in which the great plaza is quiet: by ten the coaches from Cancún have arrived, and the avenues between the buildings fill with stalls selling wooden jaguars that howl.

The pyramid in the middle is a calendar. Ninety one steps on each of four staircases plus the top platform make three hundred and sixty five, and on the equinoxes the stepped corner of the building throws a shadow down the northern balustrade that joins the carved serpent head at the bottom. Nobody has climbed it since 2006.

The rest of the site is bigger than people expect and worth the extra hour: the largest ball court the Maya built, a round observatory whose windows line up with the movements of Venus, and a sinkhole at the end of a causeway that was thrown offerings and bodies for centuries.

Then go and swim. There is a famous cenote three kilometres away, a near-perfect circular shaft with vines hanging down it, and after four hours in that heat it is the best thing that will happen to you all week.

A short last morning in the city, walking north. Start at the state government building on the square, whose upper floor holds twenty seven large canvases on the history of the peninsula, painted over more than a decade and much harder to look away from than the phrase suggests. It is free and takes half an hour.

Then out along the Paseo de Montejo, the avenue the rope barons built themselves in imitation of a Paris boulevard. The grandest of the mansions is now the regional archaeology museum, which is worth it as much for the house as for the Maya collection.

The avenue ends at a great curved monument carved out of stone in the 1950s, and after that it is time for lunch and the airport, which is twenty minutes south of the centre.