Be careful on Sundays. I'd suggest not planning to take the only or the last bus of the day. I got marooned in Ripoll this summer when the bus for Olot (connection for Girona) simply did not show up. The no-show was not an ALSA bus.
Besalu is an attractive small town. You can probably cover the entire historic district in two hours if you aren't a shopper (I coveted the metal work, but it was too large to cart home). If you want to pick up a paper map, you'll find the tourist office near the opposite end of the fortified bridge from the old town; you'll see it off to the left from the bus. There's potentially an English-language walking tour (daily? not sure), but you should contact the T.O. ahead of time if you're interested; if a French group asks first, they'll do a French tour instead. There is no bus station in town; the bus stop is basically at the edge of the old town, a bit of a walk from the T.O (back the way you've come from Girona). When I was ready to continue my trip westward, I noticed that the bus departed about 8 minutes early. Get to that bus stop well in advance! Fare from Barcelona was under 5 euros.
Ripoll is also interesting and a bit larger than Besalu. It's considerably more time-consuming to reach, but you could see it on the same day as Besalu with an early start. But check that bus schedule! I think my Girona-Ripoll one-way fare was under 15 euros. [Edit: Corrected origin point of bus ride.]
I liked Cadaques a lot--white houses and dripping bougainvillea; very "fishing village" despite all the tourist shops. If you're visiting way off season, I'm not sure how lively it would be. I found the Cadaques Museum very skippable. It would be good to have a map (paper or electronic) with you to navigate from the bus station down toward the port. The T.O.'s map sort of directs you to one side of the main street running down to the port, but the area across the street seemed equally old to me, just not as prettied-up. One-way bus fare was about 11 euros.
South of Barcelona I enjoyed Sitges. There's an interesting museum, plus a second historic building that can be visited at limited times. Research ahead of time if you decide to go. Some modernista architecture. Round-trip by train about 5 euros.
Find time for the art museum in Girona itself. It's not too large and has a very interesting collection, including architectural elements from rural churches.