Fifteen days in southern Mexico: the half of the country that does not do beaches

You arrive in a city built from scratch in 1531, on a grid, on ground nobody was living on, which is why it looks unlike anywhere else in the country. Start on the arcaded main square, with the cathedral filling one side of it.

The cathedral took most of a century, was begun in 1575 and consecrated in 1649, and its towers are the tallest of any church in Mexico. Inside it is dark, enormous and considerably plainer than what you will see in Oaxaca, which is the correct order to see them in.

Round the corner, the Biblioteca Palafoxiana was founded in 1646 when the bishop gave five thousand of his own books to the city on condition that anyone literate could read them, which makes it the first public library in the Americas. It is one long room of carved cedar shelving on three levels with about forty five thousand volumes in it, and you look at it from a rail at one end. Eat mole poblano tonight: this is where it comes from.

Cholula is eight kilometres west and has been continuously inhabited for longer than anywhere else in the Americas. The hill in the middle of it with a yellow church on top is not a hill. It is Tlachihualtepetl, a pyramid built up in stages over more than a thousand years, and by volume it is the largest structure of its kind anywhere, roughly twice the mass of the Great Pyramid at Giza.

The Spanish either did not realise what it was or did not care, and in 1594 they built the church of Nuestra Señora de los Remedios on the summit. There are eight kilometres of tunnels bored through the mound by archaeologists, a few hundred metres of which you can walk, and then a path up the outside to the church and a view of two volcanoes.

On the way back, stop at San Francisco Acatepec, a village church from the seventeenth century whose entire facade is covered in glazed talavera tile in blue, yellow and white, laid like a carpet. It is the single best example of what Puebla does with ceramics and it is four kilometres off the road.

Most of five hours southeast on a good toll road through dry mountains, and you arrive somewhere noticeably warmer, lower and more Indigenous. Oaxaca's centre is small, low and painted in colours that were chosen by committee and work anyway.

Start at the cathedral on the zócalo and then walk five blocks north on the pedestrianised Alcalá to Santo Domingo, which is the reason people talk about this city's churches. The Dominicans began it in 1572 and took two centuries, and the interior is covered, ceiling and walls, in gilded plaster figures. The genealogical tree of the Dominican founder's family spreads across the vault above the entrance in gold and paint and is the thing everybody stops under.

Then eat. Mercado 20 de Noviembre is a block of covered stalls including one aisle that is nothing but charcoal grills, where you buy meat from a butcher, hand it over to be grilled, and eat it standing with tortillas and salsa from the stall next door. Do that.

Monte Albán sits on a ridge four hundred metres above the valley floor, and the first thing to understand about it is that the ridge is not natural in its present shape: around 500 BC the Zapotecs levelled the entire hilltop by hand to make a plaza six hundred metres long. It was lived on for over a millennium and at its peak held maybe seventeen thousand people, on a hill with no water on it.

The carved slabs known as the Danzantes, on the western side of the plaza, were long read as dancers and are now generally understood to be mutilated captives. Building J, at an angle to everything else, is aligned to a star rather than to the site. Go early: there is no shade up there and the light is best before ten.

In the afternoon, back in town, the ex-convent beside Santo Domingo holds the state museum, and in it the contents of Tomb 7, which a Mexican archaeologist called Alfonso Caso opened in 1932 and found packed with several hundred objects in gold, jade, turquoise, rock crystal and bone. Next door, the ethnobotanical garden fills the old convent orchard with the plants of the state, entered only on a guided tour.

One road runs southeast from Oaxaca and everything on this day is on it. Ten kilometres out, in the churchyard at Santa María del Tule, there is a Montezuma cypress with the widest trunk of any tree on earth, something over forty metres round, and an age usually estimated somewhere between twelve hundred and sixteen hundred years. It takes ten minutes and it is not an anticlimax.

Teotitlán del Valle, twenty five kilometres on, has been weaving wool since the Spanish brought sheep and was weaving cotton for a long time before that. The workshops on the main street will show you the loom, the carding and the dyes, which are made from indigo, pomegranate skins and cochineal, the insect that lives on prickly pear and produced the red that Europe paid enormous sums for in the sixteenth century.

Mitla is at the end of the road, and it is unlike any other site in Mexico: not pyramids but low palace buildings whose walls are covered in geometric fretwork made of thousands of cut stones fitted without mortar, in fourteen different patterns. A colonial church sits on top of one of the courtyards, built from the same stone. Finish in Santiago Matatlán if there is time, which calls itself the world capital of mezcal and has some claim to it.

This is the hard leg. The overnight coach takes ten to twelve hours and climbs the whole way, or you fly and lose most of a day to airports instead. Either way you arrive somewhere that is 2,200 metres up, ringed by pine forest and noticeably colder than anywhere you have been.

San Cristóbal was founded in 1528 and named after Bartolomé de las Casas, the Dominican bishop who spent his life arguing that the Indigenous population of the Americas were people. The town below the hills is low, white and red-roofed with two pedestrian streets crossing at the middle, and it fills every morning with people from the Maya villages that begin a few kilometres out.

Do very little today. Walk up to Santo Domingo, whose baroque facade is the most elaborate in Chiapas and is best in the late afternoon when the sun is on it, and then through the craft market that fills the courtyard in front of it.

The Cañón del Sumidero is an hour down the mountain, and the way in is by boat from Chiapa de Corzo at its lower end. The Grijalva river runs through a gorge whose walls rise as much as a thousand metres almost vertically, and the two hour return trip goes deep enough in that the sky becomes a strip.

You will see crocodiles on the banks, spider monkeys if you are lucky, a great deal of plastic caught at the dam end, which the boatmen will point out and which is the honest part of the trip, and a rock face with vegetation growing in a formation that looks like a Christmas tree.

Chiapa de Corzo itself is worth the hour before or after. It has an enormous brick fountain in the square, built in 1562 in a Mudéjar style that is unique in the Americas, and a small museum of lacquerware, which is the local craft: gourds and wooden bowls painted in layers and polished to a finish that looks like enamel.

Na Bolom was the house of Frans Blom, a Danish archaeologist, and Gertrude Duby, a Swiss photographer and journalist, who lived here from the 1950s and spent decades documenting and defending the Lacandón Maya of the eastern jungle. The house is kept as they left it, with the library, the photographs and the Lacandón collection, and it is the single best thing in San Cristóbal.

The Museo de la Medicina Maya, twenty minutes north on foot, is run by an association of Indigenous healers and covers herbal medicine, bone setting and midwifery as practised now rather than as history. There is a reconstructed consulting room and a herb garden, and it is unlike any other museum on this route.

In the late afternoon, climb the steps to the Templo de Guadalupe on the hill at the eastern end of the main street, which takes ten minutes and gives you the whole town in its bowl of hills with the light going.

Five to six hours northeast on a road that drops two thousand metres, through pine forest into cloud forest into proper lowland jungle, past villages with Zapatista murals on the walls and long stretches where the only traffic is a truck. The temperature climbs about fifteen degrees on the way.

Break it at Misol-Há, which is twenty kilometres short of Palenque and is a single fall of about thirty five metres into a round green pool, with a path cut behind the water and along the cliff into a cave. You can swim in the pool, and after five hours in a van you will want to.

Arrive at Palenque in the late afternoon. The town is a working place with no particular charm and everybody stays either in it or along the road out to the ruins, where a strip of cabañas sits in the forest and the howler monkeys start at about five in the morning, which is a noise nobody is prepared for the first time.

Be at the gate when it opens at eight. By eleven the humidity is unmanageable and the coach parties are in, and the two hours before that are when the mist is still coming off the forest between the temples, which is the version of this place that people remember.

Palenque was a classic Maya city, at its height in the seventh century under a ruler called Pakal who reigned for sixty eight years. In 1952 a Mexican archaeologist named Alberto Ruz noticed that a floor slab inside the Temple of the Inscriptions had holes in it as though it had once been lifted, took up the stone, and found a rubble-filled staircase running down into the body of the pyramid. It took four seasons to clear, and at the bottom was Pakal's tomb, sealed since 683 with a five-tonne carved sarcophagus lid on it. It was the first time anyone had found a burial inside a Mesoamerican pyramid.

The palace with its four-storey tower, the Cross Group up the hill and the ball court are the rest of the morning. Then walk out through the forest path rather than the road: it goes past two waterfalls on the Otulum stream and down through the unexcavated part of the site, where mounds under the trees are buildings nobody has opened. Something like a tenth of the city has been cleared.

Seven to eight hours east by coach, or considerably less if the Tren Maya is running the section you want, crossing the base of the peninsula through Campeche state. The landscape flattens completely and the forest turns to low scrub, because the Yucatán is a limestone shelf with no rivers on it and almost no relief.

Mérida is the capital of that and it feels like a different country from Chiapas: hotter, flatter, richer, and Maya in a way that is spoken rather than worn. Arrive in the afternoon and walk to the main square, which has been the centre of a city since long before the Spanish arrived, since Mérida was founded in 1542 on top of a Maya town called T'ho and built partly out of its stones.

The cathedral on the eastern side went up between 1562 and 1598 and is the oldest on the American mainland. Across the square, the Casa de Montejo was the conquistador's own house from 1549, and the carving over the door shows two armoured Spaniards standing on the heads of two Maya, which is not subtle and was not meant to be.

Uxmal is eighty kilometres south, in the only part of the Yucatán with hills in it, and it is a different style of Maya architecture from anything else on this trip: low, wide buildings with plain lower walls and elaborately assembled mosaic friezes above, made of thousands of pre-cut stones. This is Puuc, and Uxmal is the best of it.

The Pyramid of the Magician at the entrance has rounded corners and a sloping oval plan, which is almost unique, and the legend on the site says it was built in a night by a dwarf hatched from an egg. Behind it, the quadrangle the Spanish called the Nunnery has seventy odd rooms around a courtyard and a frieze of masks, huts and serpents that goes right round it. The Governor's Palace on its terrace is the building archaeologists tend to name when asked for the finest in the Maya world, and it is aligned to the rising of Venus.

Kabah is twenty kilometres further on and is worth the extra hour for one wall: the Codz Poop, a palace facade covered in something like two hundred and fifty masks of the rain god, stacked in rows, every one of them assembled from separately carved pieces. In a region with no rivers and no lakes, the obsession makes sense.

For about fifty years around 1900 this city was one of the richest per head anywhere in the world, and the reason was henequén, an agave grown across the peninsula and processed into the rope and twine that bound the world's harvests before synthetic fibre. The plantation owners built themselves a boulevard.

The Paseo de Montejo runs north from the centre and is lined with what they spent it on: French and Italianate mansions, a few of them ruined, several of them now banks or restaurants, and one, Quinta Montes Molina, kept furnished as it was and open on guided tours. At the top, the Monumento a la Patria is a curved wall of local stone carved between 1945 and 1956 by a Colombian sculptor into a compressed history of Mexico, with a ceiba tree and three hundred and something figures on it.

In the afternoon, the Gran Museo del Mundo Maya on the northern edge of the city, opened in 2012 in a building meant to evoke the same ceiba, is the best modern museum on this route and the right place to put the last two weeks of ruins into one order.

Leave at seven. Chichén Itzá is a hundred and twenty kilometres east and it is the most visited archaeological site in Mexico by a distance, which means the difference between arriving at opening and arriving at eleven is the difference between a ruin and a fairground.

El Castillo, the stepped pyramid at the middle, has ninety one steps on each of four sides which with the top platform makes three hundred and sixty five, and on the equinoxes the afternoon sun throws a zigzag of shadow down the northern balustrade that reads as a serpent descending. Nobody has been allowed to climb it since 2006. Around it are the largest ball court in Mesoamerica, at a hundred and sixty eight metres long, with acoustics that carry a whisper the length of it, and the cenote into which offerings and people were thrown.

On the way back, stop at Izamal, which is entirely painted yellow and white and has been since the 1990s. Its convent, begun in 1561, was built on top of a levelled Maya pyramid using the pyramid's own stone, and its atrium is one of the largest of any church anywhere. Two blocks away, Kinich Kakmó is what is left of another pyramid, is the largest in the state by volume, and you can walk up it for nothing.

The last morning is a walk. Santa Lucía is four blocks north of the main square, was built in 1575 as the church for the city's enslaved and free Black population, who were not permitted to worship in the cathedral, and the small park in front of it is now where the Thursday serenades happen.

Then the market or the airport, depending on the flight. Mérida's airport is fifteen minutes south of the centre and flies to Mexico City hourly and direct to a number of American cities.

If you have a full day, the museum of anthropology in the Palacio Cantón on the Paseo is an hour, and the cenotes at Cuzamá, an hour southeast, are three flooded caves reached on a flat truck pulled along a plantation railway by a horse, which is a genuinely strange way to end a trip.