Girona, an easy hour by train or car north of Barcelona, is a college town with an atmospheric old town, with narrow, winding passageways and great architecture. It's where many of the US and international pro cyclists live and train during the bike racing season when they're not riding the Tour de France and other races.
Further north, Figueres, Cadeques, and Port Llegat are where Salvador Dali lived and created his surrealist art, and you can visit his museums and house.
San Sebastian and other towns in the Basque region that straddles the Spain/France border are where Jai Alai (the "fastest ball sport in the world") originated.
Provencal bullfights in southern France don't kill the bull, but contestants try to pluck a ribbon off the bull's forehead without getting gored, for an alternative or in addition to attending a Spanish toreo.
Segovia, a town an hour or less northwest of Madrid is worthwhile.
An alternative to train/bus/rental car is flying to some places. Vueling Air (and easyJet and others) can jet you quickly and often very cheaply around the region, although you have the usual airport issues (early check-in, going thru security, etc.), and some of the budget airlines have strict luggage policies, so check the fine print. Spanish trains require a metal detector screening of all luggage, but that's quick compared to most airport screenings.