No tourists, absurdly cheap cafés, and a spaceship better known as the Guggenheim. The only thing this Basque town lacks, Julie Myerson says, is pretension

The Martians have landed in Bilbao. Okay, that's not exactly news – by now, everyone has clocked their spacecraft, cunningly disguised as a titanium-clad Guggenheim Museum, snug in its docklands spaceport. But now I understand why they chose Bilbao. If Martians wanted to slip unobtrusively into human society, Bilbao is the best place to do it. The Guggenheim arrived and no one in this city batted so much as an eyelid. So if you expected El Goog (as the locals call it) to have transformed Bilbao into the hip, SoHo of the Basque lands, you're wrong. No, the titanium stays stolidly on the spaceship – the Bilbaoans are sticking to their blue tiles and mahogany.

So, not the hot spot you expected?

Oh no, that's the charm of the place. It's not your usual chic, cosmopolitan city. This is a real city, with real people, living real lives, with real shops, cooking real food. It is ultra cheap and unpretentiously charming. Barcelona may be the number one city in Spain but you know it's all a carefully crafted reconstruction for the international tourist market. Bilbao, on the other hand, is just itself. Sure, it has been modernised in parts, but only the way those dogged Bilbaoans wanted it. The result is a small, homogenous, sometimes messy, sometimes unexpected city, set in the hills of the north coast. And – have I made my point yet – it's startlingly cheap.

But isn't it crawling with tourists if it's so easy on the purse?

Apparently, there was a surge after the Guggenheim landed but now everyone has realised that the outside is far more impressive than anything inside. In fact, the building is downright unfair to any artist exhibited there. Jeff Koons' monstrously show-offy, giant puppy of flowers sensibly remains outside. But beyond the confines of El Goog, we didn't once hear an English voice. In the course of a long weekend, we didn't once find ourselves sitting in a restaurant alongside other Euro-travellers. It was wonderful – if tough – to find that barely a waiter or taxi driver or shop assistant spoke English. It is one of the most foreign places I have visited in Europe.

So you were a stranger in a strange and hostile land?

They couldn't be friendlier. We had only to take out our foldaway map and passing citizens would spontaneously offer us help (in fast and furious Spanish) or offer to lead us through the alleys to our chosen destination.

But where exactly were you going? What else is to see?

I'd be lying if I told you Bilbao is packed with the sights and wonders of Iberia. It's a small place, an industrial centre with a long, snaking dockside. The main city divides into two: the Casco Viejo is the old bit with winding, car-free streets and shops straight out of the 1950s, selling aprons and wedding dresses and dusty millinery. In the heart of the Casco is the cathedral – but even this is pocket-sized, simple and unshowy, its Saturday steps dotted with nuptial rice. The true heart of the Casco Viejo is the Plaza Nueva, a huge colonnaded square, housing just cafés and restaurants. On our first day, there was an impromptu juggling convention in progress: 20 teenagers excitedly leaping about – not for the tourists, just for the fun of it.

Sounds like it's all hustle and bustle. Is there anywhere to relax?

The key is to take frequent café stops and there are certainly plenty of places to take them. The best spot in the Plaza Nueva is the Belle Epoque-style Victor Montez. Sit and sip your Fino and watch the black-clad Bilbaoan toddlers run races under the evening sky. The cafés seem permanently full, whether for a simple drink or a flood of pintxos, the local tapas specialities. It's worth mastering some Spanish (or at least carrying a hefty dictionary) if you want to make the best possible choice. During the evening, those too antsy to sit sashay round the colonnade, meeting, colliding, talking, in and out of bars.

What about the shopping?

As it became richer in the 19th century, Bilbao realised it needed more space. So it spread into the Ensanche ("The Extension") over the river. Cross the ornate, lamp-garlanded bridges and you'll find a battalion of proper fashion shops, bargain designer shoes and, of course, some wonderfully grand and retro cafés.

I don't know if you've noticed but you're talking about food and drink a lot

That's what you do in Bilbao. Forget galleries, shop if you want to (even the international designer prices are about two-thirds of what you'd pay in Britain) – but mostly just drink and eat. It's what the Basques do best. There's good solid Basque cooking and there's New Basque cuisine. After a selfless inspection, I think I prefer the old-fashioned basic. But, wherever you eat, remember to no Bilbaoan would even contemplate lunch until 1.30pm, or dinner untill 10pm.

You must have run up quite a bill

Do I have to say it again? That's the biggest attraction of all: Bilbao is frighteningly cheap. And it's not just the exchange rate. We struggled to order more and more tapas, and yes, another bottle of wine, and still it was never more than £20 for two. Most larger cafés will offer a Menu del Dia – three courses, coffee, wine or water for less than 2,000 pesetas (£8). And it's not just the food. A taxi across town will be around Pts500 depending on the time of day. Norman Foster has designed a clean, funky tube system, with escalators emerging on to the pavements like transparent caterpillars. Use it once just to see the sleek, stonework platforms (and 100 per cent absence of litter) but the peseta saving is barely worth it.

Okay, I've emptied my wardrobe, I've gone on a diet, how can I get there?

That's the other joyous thing. All of this is a mere 90 minutes plane ride away (or a 36-hour ferry crossing if you fancy seaboard romance). We flew with Kirker Holidays (020-7231 3333) which offers an ultra-comfortable, three-night package at the four-star Hotel Indautxu for only £398 per person, including return flights, transfers and admission to the Guggenheim. This is unspoilt, budget Europe at your fingertips – and a great antidote to the approaching British winter.