Four days in Montevideo: a capital that walks its waterfront with a thermos under one arm

Plaza Independencia is the hinge of Montevideo: the Ciudad Vieja on one side through an eighteenth century gateway, and the long commercial avenue of 18 de Julio running east on the other. In the middle stands a bronze of José Artigas on a horse, and underneath him, down a flight of marble steps, is his mausoleum, guarded around the clock by two soldiers who change with considerable ceremony.

On the eastern corner is the Palacio Salvo, a 95-metre Art Deco tower finished in 1928 that was briefly the tallest building in South America and still looks like something a supervillain would live in. It stands where the café once was in which La Cumparsita, the most played tango ever written, was first performed.

Then Teatro Solís, a block into the old town. It opened in 1856, it is where every Uruguayan of consequence has performed or been mourned, and its interior of red plush and gilt has been carefully restored. If nothing is on, the guided tour runs several times a week and takes you into the auditorium and backstage.

Walk into the Ciudad Vieja under the Puerta de la Ciudadela, the last surviving fragment of the city wall that was pulled down in the 1830s. Behind it, Sarandí runs the length of the peninsula as a pedestrian street of nineteenth century facades, book shops, buskers and half-finished restoration.

The Museo Torres García is on that street. Joaquín Torres García spent decades in Barcelona, Paris and New York before coming home, and in 1943 he drew South America with the south at the top and wrote that the north is our south, which became the most reproduced image in Uruguayan art and a small manifesto about who gets to decide which way up a continent goes. The museum holds his paintings, his wooden toys and the drawing itself.

In the afternoon, the Museo Andes 1972, a few streets away. In October 1972 a plane carrying a Uruguayan rugby team to Chile came down high in the Andes; sixteen of the forty-five people on board were still alive when they were found seventy-two days later. The museum is small, made largely of objects the families lent it, and it is told plainly and without sensation. It is the most affecting hour in Montevideo.

Eat at the Mercado del Puerto at the end of the peninsula, a nineteenth century iron market hall now full of parrillas grilling over wood. It is touristy and it is also where the beef is best.

Take a bus or a taxi out to the concrete bowl that was built in 1930 to hold the first World Cup and to mark a century of the Uruguayan constitution. Uruguay won that tournament, beating Argentina in the final here in front of a crowd that had come across the river by boat, and the country has never entirely stopped talking about it. A second title in Brazil in 1950 confirmed the habit.

The football museum is inside the stadium and the ticket usually gets you out onto the terraces and down to the pitch when there is no match. It is shirts, boots, trophies and photographs, and it makes sense of why a country of three and a half million people expects to win.

Then go down to the water and walk. The Rambla runs twenty-two kilometres along the shore, and the stretch from Parque Rodó through Punta Carretas to Pocitos is the best of it: fishermen, cyclists, dogs, groups sitting on the wall with a gourd and a thermos, and a red sun going down over the estuary. Pocitos beach at the end has the big Montevideo letters on the sand that everybody photographs, and a line of cafés behind it.

The Palacio Legislativo is twenty minutes north of the centre and it is the most extravagant building in Uruguay, finished in 1925 for the centenary of independence and lined throughout in Uruguayan marble. It houses the parliament of a country that has been continuously democratic for most of its history and is loudly proud of it. Free guided tours run most weekdays, usually in Spanish with English at set times, so check before you go.

Then head east towards the airport and stop in Carrasco, which is a suburb of enormous trees, old villas, small bookshops and cafés with tables outside, spread along the beach at the far end of the Rambla. The old casino hotel there was built in the 1920s when this was a resort for Argentines, and the neighbourhood has kept that unhurried feeling.

The airport is ten minutes further on, which makes this the natural last hour.