Subject: Barcelona, Catalonia
In general, Costa Brava is more scenic in terms of landscape. Tossa and Cadaques are quite nice. Cadaques is also located close to Figueres, where you have the Dali museum. From Cadaques you can also cross the border and visit some of the villages on the French side, such as Colliure. On the South, probably Tarragoan is the most interesting place, specially for its Roman monuments. I don't think Lerida (Lleida in Catalan) is worth the drive. Closer to BCN you can visit Girona and Besalu (on the North) which are quite nice. Both of them are towns with a medieval area. Girona is a larger city while Besalu is smaller. Another interesting area to visit, quite close to Tarragona, but not on the coast is the Ruta dels monestirs, which include Santa Creus, Poblet and (somewhat farther) Vallbona de les Monges. These are three monastaries Carcasonne is definitly worth it, but it's more or less a 4 hour drive from Barcelona. Perpignan is OK, but not really marvelous.

What you want to do depends a lot on what type of transportation you're going to use. If you're driving, most of the places are very accessible through autopista and none of them should take you more than 2-3 hours to get there (without rushing). However, if you're planing to use public transportation it may be a little more difficult. Definitely, there are either train sor buses (or both) from Barcelona to any of those places, but if you want to visit several of them it may be a little more difficult to go from one to another.