Four days in Quito: the old town Spain built and nobody ever knocked down

Go slowly. You have arrived at nearly three kilometres above the sea and the old town's streets are steep, so give the first afternoon to three things within five minutes of each other.

Plaza Grande first, to sit down. The square is the political centre of Ecuador and behaves like a public living room: shoeshine stands, chess, brass bands, retired men arguing. The white colonnade on the west side is the Palacio de Carondelet, where the president works.

Then La Compañía, half a block away, which is the one building in Quito people travel for. The Jesuits took over 160 years to finish it and covered nearly every interior surface in gold leaf over carved wood, so the effect indoors is less like a church than like standing inside a reliquary. A fire in the 1990s destroyed much of the roof and vaults, and the restoration, helped by the Getty, is why the gilding looks so fresh.

In the late afternoon walk down to Calle de la Ronda, a narrow cobbled lane below Plaza Santo Domingo restored in 2007 with the residents still living in it. Galleries, small patios, canelazo sold hot from doorways. It is quietest early and best around dusk.

San Francisco opens the day. The Franciscans were the first order here, which is why the city's full name is San Francisco de Quito, and the complex they began in 1537 still takes up an entire side of its own square. The famous thing inside is Bernardo de Legarda's Virgin of Quito on the main altar, a winged Madonna standing on a serpent, and the copy of her on the hill outside is why people call Quito the city with a winged virgin. Pay for the museum next door: it runs through the cloisters and up to the choir, and a staircase from there gets you onto the roof and the bell tower.

Cross the square to the Casa del Alabado, a restored colonial house holding a private collection of pre-Columbian ceramics. It is arranged by theme rather than by culture or century, which sounds like a gimmick and works: shamans in one room, the dead in another, so you see the same ideas recurring across two thousand years and half a dozen peoples. An hour and a half, and there are guided tours in English through the day.

Walk north for the Basílica del Voto Nacional in the afternoon. It was begun in 1892, is still technically unfinished, and is the largest neo-Gothic church in the Americas. Look up at the gargoyles before you go in: instead of European monsters they are Galápagos tortoises, iguanas, armadillos and condors. Then buy the tower ticket. You cross a plank walkway above the nave, climb a steep steel ladder inside the clock tower and come out on an open platform with the whole valley below you. It is not for anybody who dislikes heights.

Cotopaxi is an hour and a half south down the Panamericana, and at 5,897 metres it is one of the highest active volcanoes on earth. What makes it worth the day is the shape: an almost perfect cone with a glacier on it, standing alone above a plain of tussock grass at around 3,600 metres with nothing to interrupt the view.

Go with a driver or a small tour rather than by bus; the park entrance is well off the main road and there is no service inside it. Stop at the visitor centre first for the relief model and the stuffed condor, then drive up to Limpiopungo, a shallow glacial lagoon just under the snowline with the volcano reflected in it on a still morning. The walk around the water is flat and takes an hour, and at this height that is quite enough.

Go early. Cotopaxi is usually clear at dawn and wrapped in cloud by lunchtime, and by mid afternoon you may not know it is there at all. The volcano has been restless since 2015, the summit route has been closed for long stretches, and the park itself occasionally shuts at short notice, so check the day before rather than the week before.

The TelefériQo runs from the western edge of the city to about 4,000 metres on the flank of Pichincha in under twenty minutes, which is a brutal gain in altitude and exactly why it goes on the last morning rather than the first. On a clear day the row of volcanoes down the eastern horizon is the single best view anybody gets of Ecuador without walking for it.

Be at the bottom station when it opens. The mountain clouds over reliably by late morning and the queue builds behind the tour buses. At the top there is a short paved loop, a swing over the drop that everyone photographs, and trails running on towards Guagua Pichincha, which is a serious hike and not a morning's stroll.

Then down, collect the bags, and allow properly for the airport road. Tababela is 40 kilometres out and the traffic on the ring road can turn 45 minutes into ninety without warning.