Now, not gonna list all the touristy stuff, for that head to the tourism websites of both places; I will instead mention a few 'other' things I believe you might enjoy:
While in Besalú:
- Obviously, you have a really great photo opp if you follow my instructions and enter the town thru the stone bridge, and walk under the iron gate into the "fortress", your kid will be mesmerised. Have your best stories about dragons and princesses at hand!
- There are a handful of shops with souvenirs spread throughout the town, but not those tacky cheaply-made plastic Chinese imports, but real artisan-made little details that will truly inspire you: leather goods and lots of medieval-related items which exploit the glorious past of this key town. One particular toyshop comes to mind, it's called El Drac Màgic (Catalan for the Magic Dragon), it's near the bridge, in Carrer del Pont Vell, 15. You'll find all sort of wooden arches, swords, capes and shields and even fake armour for your kid so he becomes a true knight.
- Relax having a coffee at the terrace of "10 del Pont" (roughly:"deh-oo-duhl-pont") in Baixada de la Mikweh, a narrow street near the toyshop with great views of over the bridge and the river. Located just above the remains of the medieval Jewish Baths of Besalú.
- At the beginning of September, Besalú celebrates an spectacular Medieval Fair which attracts many families.
While in Girona:
- Have an ice cream in Rocambolesc, the latest venture of the Roca Brothers (they're from Girona). Their restaurant El Celler de Can Roca has been considered the Best in the World by the for several years. Yeah, I'm bragging about my fellow Catalans, of course, but it's not an exaggeration, it's true, check it! :) Your kid will love this Willy Wonka-esque gelateria!
- Relax having a coffee/tea and a pastry at La Terra, a quirky little coffee shop located by the river. Don't sit by the entrance, head towards the back and get a table by the window, facing the river.
- An idea for a late-afternoon snack kids do love... a chocolate crêpe at Crêperie Bretonne. They even have a real minibus inside the restaurant, my niece used to like it when she was younger.