Bilbao: the titanium museum, pintxos in Plaza Nueva and a bridge that carries people

The Guggenheim Museum Bilbao, opened in 1997, is one of the most famous buildings of contemporary architecture. Frank Gehry's titanium curves change colour with the light and weather and look like a ship, a fish or a metal flower depending on the angle. The impact was so great that people speak of the «Guggenheim effect» to describe cities transformed by a single building.

At the entrance stands Puppy, a giant flower-covered dog by Jeff Koons that changes its coat with the seasons. On the river side is Maman, Louise Bourgeois's enormous bronze spider, between whose legs everyone takes photos.

Inside, exhibitions change through the year, and the large gallery with Richard Serra's steel sculptures is a physical experience: you walk inside metal spirals that seem to move. Allow two to three hours.

The Nervión river, which locals call the ría, runs through the city and was once its industrial heart. Today its banks have promenades, gardens and modern buildings, and walking along the estuary from the Guggenheim to the old town is one of the best ways to get to know Bilbao.

The Zubizuri Bridge by Santiago Calatrava is white, curved and pedestrian, with a glass deck that, according to locals, gets slippery in the rain. Further on, La Salve Bridge has a large red arch by a French artist that embraces the museum.

At night, with the bridges and buildings lit up and reflected in the water, the estuary is very beautiful. It's the ideal after-dinner walk.

The Casco Viejo, the old town, grew around seven parallel streets, the Siete Calles, near the river. The streets are narrow, with traditional shops, churches and bars, and the Cathedral of Santiago marks the centre.

Plaza Nueva, a nineteenth-century arcaded square, is the heart of Bilbao's pintxos. The bars under the arches fill their counters with little edible works of art, and on Sunday mornings there's an antiques and stamp market.

By the estuary is the Ribera Market, a large covered market with fish, meat and vegetable stalls and an area of pintxo and food stands. Try bacalao al pil-pil, bacalao a la vizcaína and txangurro, stuffed spider crab.

The Artxanda funicular, opened over a century ago, climbs in a few minutes from the centre to the hill of the same name. At the top is a viewpoint with the most complete view of the city: the estuary, the Guggenheim, the bridges and the green hills around.

On the hill there are also parks, grill restaurants and paths for walking. It's where Bilbao locals go on Sundays, especially for long lunches of meat and fish cooked over coals.

In the late afternoon, the view with the city lights coming on is one of the best. Take the funicular down and head to the bars in the centre.

The Vizcaya Bridge, between Portugalete and Getxo, opened in 1893 and is the world's oldest transporter bridge still in service: a suspended gondola carries people and cars from one bank to the other. It's a UNESCO World Heritage Site, and you can cross in the gondola or along the walkway on top.

San Juan de Gaztelugatxe, about 40 minutes away, is an islet joined to land by a stone bridge and a zigzag staircase of more than two hundred steps, ending at a small hermitage. It became famous as a setting for a very well-known fantasy series. Access is controlled at certain times, so check before you go.

Gernika, about half an hour away, is the town bombed in 1937 that inspired Picasso's painting. It has a peace museum and the tree that symbolises Basque liberties. A private tour lets you combine the coast, Gaztelugatxe and Gernika in one day.