Four days in La Paz: a capital poured into a canyon, with cable cars for a metro

Arrive, drop the bags, and do three things in six blocks.

San Francisco anchors the lower end of the old quarter. The current church went up in the eighteenth century after snow brought the first one down, and the stone was carved by indigenous masons who filled the facade with Andean things the friars had not asked for: parrots, masked faces, chirimoya fruit, pumas. The monastery beside it is now a museum, and the ticket includes the choir, the cloisters and a walk out onto the roof.

Uphill from the plaza is Calle Linares and the Mercado de las Brujas. The stalls sell dried llama foetuses, which are buried in the foundations of a new house as an offering to Pachamama, along with amulets, sweets for burnt offerings, herbs and soapstone charms. It is not a performance for tourists; the customers are mostly paceños. Photograph the stalls only if you ask.

Finish at the Coca Museum, two rooms on Calle Linares explaining the leaf's four thousand years of Andean use, how the alkaloid was isolated in the nineteenth century, and what the war on drugs did to Bolivia. The labels are in Spanish and they hand you a full translation at the door.

Plaza Murillo is the political centre and a good deal calmer than the history attached to it. The cathedral fills one side, the old presidential palace another, and the square is named for Pedro Domingo Murillo, hanged here in 1810 after leading the first uprising against Spain. The clock on the congress building runs backwards, which was a decision rather than a fault.

Two blocks away is MUSEF, the national ethnographic and folk museum, and it is the best hour in La Paz for understanding the country you are in. Bolivia has three dozen recognised indigenous languages, and the museum's collections of masks, weaving and ritual objects treat them as living rather than historical, with the weaving room in particular showing how much information a textile carries.

In the afternoon get on the cable car. Take a line from the canyon floor up the wall and change once, and you rise out of the city until the whole gash in the earth is laid out below with Illimani behind it. Get out at the top in El Alto, which is a different city: flatter, higher, colder, overwhelmingly Aymara, and home to the Feria 16 de Julio, one of the largest street markets in South America, which spreads for kilometres on Thursdays and Sundays. Keep your bag in front of you and go back down before dark.

Tiwanaku is about seventy kilometres west of the city on the altiplano near Lake Titicaca, an hour and a half each way, and it is the reason Bolivia has a pre-Inca history that people argue about. It was the ceremonial capital of a state that dominated the southern Andes for several centuries and had already collapsed before the Inca came anywhere near it.

What survives is stonework rather than architecture: the stepped platform of the Akapana, the sunken temple lined with carved heads of dozens of different faces, the Kalasasaya enclosure with the Ponce monolith standing in it, and the Gate of the Sun cut from a single block of andesite with a figure carved above the lintel that nobody can name with confidence. The joints in the stone are so fine that the site attracted a century of nonsense about who really built it; the answer is the people whose descendants are selling you lunch in the village.

Go with a guide or a tour, because the site is flat, wind-scoured and almost entirely unlabelled, and the two museums by the entrance hold the pieces that make sense of it. At 3,800 metres with no shade, take a hat, water and something windproof.

The Valle de la Luna is about ten kilometres south, past the wealthy suburbs where the air is thicker, and it takes twenty minutes in a taxi. It is not a valley so much as a hillside of soft clay and sandstone that rain and wind have cut into hundreds of thin spires and funnels, pale grey and beige, with paths threading between them.

There are two marked circuits, a short one of about fifteen minutes and a longer one nearer three quarters of an hour, and the longer one is worth it. Go in the morning while the light is still raking across the formations and before the tour buses arrive.

From there it is back up through the city and out to the rim, which is a long climb in traffic. Leave more time than the distance suggests, and considerably more if there is a march or a blockade announced.