In the space of a precious weekend or over the few days of half-term, is it worth the effort of hauling yourself on to a plane (not to mention the palaver of getting to the airport in the first place) to take a city break? Wouldn’t it be more restful just to slob out at home? Well, sometimes, yes. But a new place with unfamiliar sights can be a powerful restorative; a different climate can shift stagnant patterns. And with cheaper air travel, it’s become more affordable.

Bilbao is a case in point. After a flight of less than two hours from a wet London, we looked out over a sparkling sea and sandy beaches that guard the entrance to the Nervi“n estuary on which the city stands. One of us had paid a rock-bottom Go fare, the other had decided to tag along later and was still smarting at the extra cost of not making up her mind quickly enough. But the bright, clean airport and the short taxi ride into town (about e15) through gentle green hills began to soothe that. The simple hotel we’d picked at random from the Rough Guide was fine, too: it was on the edge of the Casco Viejo, or old town, and near the river.

We’d come to see the much trumpeted Guggenheim Museum - the space-age fortress of modern art designed by Frank Gehry that, since it opened five years ago, has done so much to pull Bilbao out of its decline as a post-industrial city. And it didn’t disappoint. What we hadn’t realised (we only started reading the guidebook on the plane) was how much else there was to discover. Two days just wasn’t long enough.

The old town is all as picturesque as you could wish for and bursting with shops, bars and restaurants. Although the streets are medievally narrow and the buildings come in a variety of gothic, 19th-century swirls and Art Deco slices, many of the shops sell high-fashion clothes and leather goods - some at designer prices, but a few are quite reasonable.

From what we’d seen through restaurant windows, Basque cuisine looked too substantial for this first evening, so we dined on wine and pintxos, the Basque version of tapas.

Next morning, after coffee in the Art Nouveau grandeur of the Cafe Boulevard, by the Punto de Encuentro bridge, we walked along the riverside towards the Guggenheim. The quaysides are being redeveloped and there are plenty of green spaces and benches to rest. A little way past the helpful tourist information office where we stocked up on maps and leaflets, a surprise: the Zubizuri pedestrian bridge - a graceful modern curve with a sense of humour.

Crossing it, we were soon circling the Guggenheim, which floats on its pool next to the river like an extraterrestrial apparition in titanium. At the main entrance away from the river, there’s an unexpected cause to smile: Jeff Koons’s huge puppy made of pansies, bigger than a bus and blooming ridiculous. Pictures don’t prepare you for what a laugh it all is - and inside the museum, too, while the spaces amaze and the changing exhibitions are challenging, there’s a light-hearted feel: we’re alive, let’s have fun, it seems to say.

After a day exploring every sinuous corner, going out for lunch and coming back in, as the day ticket allows, we sat by the river, trying to summon up the energy for the short walk back. But though night was falling and the museum was closed, the show wasn’t over. With a whoosh, giant flames roared out of the pool, reflecting on the shiny walls and the water. We jumped, then gaped - where had they gone? A few minutes later, just when we decided to wait no longer, they were back, then disappeared again as unpredictably as they’d arrived. After that, the attractions of late-night shopping along the Gran Via paled, and a vast Basque dish of salt cod washed down with cider from wooden barrels beckoned in the old town.

And what of the Museo de Bellas Artes, Bilbao’s home for more traditional art? What of the Fosteritos, the Norman Foster designed entrances to its metro system? What about the gothic Santiago cathedral, the Sunday market in the Plaza Nueva, or taking the funicular into the green hills that wrap round the city? There just wasn’t time. But they’ll be there for my next visit.

Go, which will merge with easyJet in the new year, flies to Bilbao from London Stansted up to twice a day, from pound;50 return (lowest fares available on the Internet) 0870 607 6543; www.go-fly.com The Rough Guide to Spain, pound;13.99. Details from the Spanish Tourist Office: 020 7486 8077; www.basquecountrytourism.net The Guggenheim Museum, Bilbao, is open daily except Monday from 10am to 8pm; entry e7 (children under 12 free); www.guggenheim-bilbao.es.