Our best advice is to hire a car. Hire from the airport to make it easy; there are toll roads connecting the major towns including Girona and Barcelona. But don't hire a tall, wide 4x4 or similar because some of the prettiest towns have very narrow roads and tight corners. For car hire see our car rental recommendations.
Our tip, if you like driving, is to tackle the dramatic road from Figueres to Cadaques, with sheer drops on either side, or to drive the Collada de Toses from Ribes to Puigcerda which is a mountain route with switchbacks and vertiginous drops straight from a James Bond film.
Bike hire is very popular in the region too, both mountain bikes and professional cycles.