try this site, it's excellent:
they have some maps of suggested pinxtos tours (pinxtos is basque for tapas).
There's a place called Txepexta that's pretty awesome.
You'll mostly want to drink the fizzy white wine that's the local specialty, but if you feel like cocktails there's an awesome tiny pinxtos place in the Gros neighborhood, Garbola Bar, where the bartender fancies himself a cocktail specialist and makes elaborate mojitos, etc. with his own homemade syrups while blasting 80s music.