Ten days in Peru: sea level to 3,400 metres, one step at a time

Most flights from Europe and North America land in Lima before dawn, so the first day starts whenever you wake up. Miraflores, up on the cliff, is the easy landing: flat, walkable and full of places to eat.

Lunch is when Peruvians eat ceviche, because the fish is cured in citrus for a few minutes rather than overnight and the good places sell out by three. Order the leche de tigre, the marinade left in the bowl, as a glass alongside it.

Then the pyramid in the middle of the district, and an early evening in Barranco, the old seaside quarter next door where the wooden houses and the painted walls are.

One day for the old city. Pizarro laid out the main square in 1535 and the four sides have held the same institutions ever since: the presidential palace, the cathedral, the archbishop's residence and the city hall. The guard is changed in front of the palace at 11:45, watched from the square, free and unhurried.

The Franciscan church a few streets east is the one people remember. Its library holds thousands of vellum-bound volumes, and its crypt holds the bones of an estimated twenty-five thousand people, disinterred and stacked by type when the cemetery filled.

In the afternoon, cross to Pueblo Libre for the museum that makes sense of everything you are about to see in the mountains: three thousand years of coastal and Andean cultures, laid out in order, in a mansion built over a pyramid.

A morning flight down the coast and inland, an hour and three quarters, landing among volcanoes. The taxi into Arequipa runs at a posted flat rate and the centre is fifteen minutes away.

The old town is five blocks square and almost entirely built of sillar, which is white when it is new and pale grey when the sun goes off it. Start on the main square, which has arcades on three sides and the cathedral filling the fourth, and go up onto the cathedral roof for the volcanoes.

The Jesuit church a corner away has the facade that Arequipa is known for: soft volcanic stone carved into vines, faces, birds and shapes that came out of Andean rather than European imagination.

Santa Catalina opened in 1579 and stayed closed to the outside world for almost four centuries, so what is behind its walls is not a building but a district: lanes with street names, painted in ochre and cobalt, with cells, kitchens, cloisters and a laundry of stone basins. Give it three hours and go early, before the light gets hard.

Lunch belongs in a picanteria, the Arequipa institution that opens at midday, cooks one thing especially well and stops when it runs out. Rocoto relleno, a stuffed hot pepper baked with cheese, and chupe de camarones, a river prawn chowder, are what the city is famous for.

The afternoon is one small museum and one exhibit: a girl of about thirteen who was taken up Ampato and sacrificed some five hundred years ago, and who came down off the mountain frozen in 1995 when ash from a neighbouring eruption melted the ice cap.

An hour in the air and you are eleven hundred metres higher. Take the afternoon at the pace of somebody recovering from something, because in effect you are: your blood will spend the next two days making up the difference.

The main square is flat, five minutes from most hotels, and enough of a first day. The cathedral on its northeast side is really three churches joined together, hung with hundreds of canvases from the Cusco school, including a Last Supper with a roast guinea pig on the table.

Eat early, drink water rather than pisco, and go to bed. Tomorrow is uphill.

Go to the sun temple at opening. The Spanish found its walls plated in gold and a garden of life-size gold and silver maize, took all of it, and put a Dominican convent on the foundations. What survives underneath is the best stonework the Incas ever cut, tapered and curved and fitted without mortar, and the seam where the two building cultures meet is a metre above your head.

In the afternoon, climb. It is a steep twenty-five minutes from the square to the ridge, or a five-minute taxi if the height has other ideas. The zigzag ramparts up there use blocks of over a hundred tonnes, and only about a fifth of the complex is still standing: the Spanish carted the rest downhill to build the city.

A kilometre further on, a limestone outcrop has been carved with channels for pouring liquid, a passage through the rock and an altar in a cave. Shared minibuses run back down to the centre for small change.

The Sacred Valley is the stretch of the Urubamba below Cusco, six hundred metres lower, warmer, and where the Incas grew the maize that fed the capital. The drive over the pass and down into it takes about two hours by shared minibus.

Ollantaytambo is the clearest surviving example of an Inca town still lived in, laid out on its original grid with water running in the channels that were cut for it. Terraces climb the mountain above it to an unfinished sun temple of six enormous pink granite slabs, dragged across the river from a quarry on the opposite slope. In 1537 Manco Inca held this ground against Spanish cavalry by flooding the plain below, one of the few Inca victories of the whole war.

On the far side of town, a free path climbs to a row of storehouses set high where the wind kept grain dry. It is quieter than the main site and the view back across the terraces is the one worth carrying a camera for.

A slow day between two hard ones. Hatunrumiyoc, the lane running east off the cathedral, is one continuous Inca wall, and set into it is the block everybody stops for: twelve sides, twelve angles, no gap anywhere along the joints.

Two small museums fill the rest of it without any climbing. One holds the region's pre-Inca and Inca material, mummies and drinking vessels and deformed skulls, in a colonial mansion by the cathedral. The other is a weaving centre that shows the difference between what the villages around Cusco produce by hand and what is sold on the square, and pays almost all of the price to the woman who made the piece.

Then pack, because tomorrow starts early and you will not be sleeping here.

Back down the same road to Ollantaytambo, and this time you get on the train. It follows the Urubamba as the river drops, the valley narrows and the vegetation changes from dry Andean scrub to something closer to cloud forest, all in about ninety minutes. Passports are checked at the station.

Aguas Calientes is a town of hotels, restaurants and a railway line down the middle, and it is easy to be sniffy about it. It is also two hours closer to the ruins than Cusco is, which tomorrow will justify.

Spend the afternoon walking the tracks north to a private garden of orchids and a waterfall, then take the hot springs at the top of the town before dinner. Buy tomorrow's bus tickets today and confirm your entry hour.

The buses start climbing before sunrise and take about twenty-five minutes up the switchbacks; the queue forms earlier than you expect and moves faster than you fear. Walking up instead is roughly ninety minutes of steep stone steps.

Machu Picchu was built around the middle of the fifteenth century, most likely as a country estate for the emperor Pachacutec, and was left within a hundred years without the Spanish ever finding it. Terraces hold the ridge in place, spring water runs through sixteen carved fountains, and the site sits on a saddle between two peaks with the river four hundred metres straight down.

You follow a numbered one-way circuit, so what you see is set by the ticket rather than by wandering. Slow down at the curved tower over the royal tomb, at the carved granite pillar on the upper terrace, and at the small chamber with a condor's head cut into the floor. Then the bus down, the train back up the valley, and Cusco or a flight out of it by evening.