I second Harold's Girona suggestion - wonderful narrow, steep passageways around the old town, wonderful plazas, a great walking location that's just an hour away from Barcelona by train or car. You didn't mention whether you were using your own car or public transportation, but seeing some of France is doable. If you're renting a car in one country, remember that turning it in in a different country could result in hefty fees, if the company even allows it. Going by air or by fast train could allow you to reach more-distant places without taking too much time away from those places. We drove this past November up to Figueres, Cadaques (great spot on the water, with verdant hills all around), and Port Llegat for the Dali museum & his & Gala's house and enjoyed that.
I haven't been there, but it seems to me that just north of the border in France, Collioure is one of Rick Steves' special "back doors" and we hope to get there some day. I've visited other places in southern France, though, and don't think I would go out of my way for Perpignan or Montpellier. Seeing the rice and salt operations in the Camargue were interesting, though. We spent a night in Sete (it was late and we needed a room) but would not go there again. Depending on how far you wanted to go and how fast you could get there, even Nice could be worth considering!