Barcelona - An hour to the south by train and the capital of Catalonia with an endless list of things to see and do.
Figueres - A town approximately 30 minutes to the north by train with the famous Dalà museum and an active Old Town core.
Hostalric - An old walled town south of Girona.
Madremanya - Old, compact Medieval village boasting a Michelin rated restaurant. About 15 minutes from Girona by car.
Torroella de Montgrà - A pleasant old town that was once the capital of the Empúries kingdom. Now it sits at the base of a mountain that goes up to a castle. A good day hike for those inclined.
Tossa de Mar - While unfortunately deeply slathered in beach tourists, the original old town of the city is quite lovely to walk.