The New York Times over the last 2 months wrote two interesting articles about gastronomy on the Spanish side of the Basque country, 2 destinations easily reachable for the evening or the day for travellers staying on the French side, in the St Jean de Luz/ Biarritz coastal stretch:
1) in the little town of Hondarribia, located right on the Spanish/French border: A Dining Explosion in a Tiny Basque Town at http://www.nytimes.com/2010/08/01/travel/01Next.html?emc=eta1 Some good addresses for sure. Hondarribia is not as small as what the article mentions. It has been very popular for many years among the habitants of Irun, as Hondarribia is like a fancy subburb by the beach of Irun, the busy commercial border town. Hondarribia is rich in history ( ie the land of many battles) and its medieval architecture offers a treat to the eyes. While staying in France, on the French side of the Basque country, it is a very popular and easy to get to destination for a few drinks and pinxos ( basque word for tapas): you hop on a boat from the French town of Hendaye to cross the Bidasoa river that separates the two countries. Make sure you take a stroll up the hill all the way to the old town, la parte vieja, after you warm up your senses with a couple of pinxos and a glass of txaculi in the fisherman's village called la Marina
2) in the city of Bilbao well known for its Guggenheim: In Bilbao, it's not just the Museum at http://www.nytimes.com/2010/10/10/travel/10Choice.html?emc=eta1 The renaissance of this city includes some amazing contributions in all price categories by various chefs. If coming from the French side on a full day outing to Bilbao, do spend the time to go to the Casco Viejo, the old quarter of town, reachable via a nice walk along the river from the Guggenheim.
No matter what, even if you are not a committed foodie, do take the time to enjoy a few pinxos in the company of locals.