100% agree with Nick, between northern Catalonia, the Pyrenees, and Languedoc (across the border) you have more then enough to fill a week or two at least. Here is a rough itinerary for a road trip through northern Catalonia and the Languedoc region of Southern France, I had previously drawn up:
DAY 1-
Start in Barcelona, rent car, and drive north to
-{ Girona: An ancient city in northern Catatonia. Has an impressive Cathedral, towering medieval walls, narrow winding streets, and one of the best preserved Jewish Quarters in Europe.
Sleep in Girona - 2 nights
DAY 3-
Drive north to
-{ Besalú: Well preserved medieval town showcasing Romanesque and Gothic architecture. The centerpiece is the impressive medieval bridge.
Turn West to Andorra la Vella
-{Stop in the medieval village of Castellfollit de la Roca
Sleep in Andorra la Vella - 2 nights
DAY 4-
-{Explore Andorra and the nearby Early Romanesque churches in the Vall de Boí, a UNESCO World Heritage Site.
DAY 5-
Drive north through the Pyrenees
-{Stop at Foix and check out the Château de Foix
Continue north to Toulouse
Sleep in Toulouse - 2 nights
DAY 6-
-{Explore Toulouse: The fourth-largest city in France, nicknamed the "pink city" because the old center of the city is built with terracotta bricks. The UNESCO designated ancient Basilica of St. Sernin is a highlight.
DAY 7-
Drive south east to Carcassonne
-{Explore medieval fortified town of Carcassonne
Continue east to Béziers
-{Explore Béziers: The historical center, built on a hilltop, is a great place for a stroll through the little squares and picturesque streets. Check out the lovely cathedral (with a sinister past)
Sleep in Béziers
DAY 8-
Drive south to Narbonne
-{ Narbonne: A city with deep historical roots from the Roman and early Medieval times, the highlight being the Archbishop's Palace.
Drive south towards Spain
-{Check out Narbonnaise en Méditerranée Natural Park: Diverse protected landscape with good hiking trails through beaches, lagoons, and vineyards
Continue south to Figueres
-{See Dali museum in Figueres: Extensive collection of Dalí's artwork, from paintings to sculpters and everything in between.
Return car in Girona and sleep in Girona
DAY 9-
-{Explore more of Girona in the morning and pack
Take the AVE high speed train to Barcelona and fly out of Barcelona
Note that this is a pretty rough itinerary, it's more meant to inspire some ideas about potential destinations for your road trip. Hope this helps :)