Girona's medieval district is quite large. You can spend a lot of time just wandering around. You can walk part of the way around it on the walls, as well. There's a decent Museum of Fine Arts (not as large as Barcelona's MNAC, which I'd recommend if you have to choose just one of them) and a Jewish History Museum that I haven't seen. The Cathedral and the nearby St. Feliu are important historic churches.
Figueres, location of the Dali Theatre-Museum, is an easy side trip from Girona by train. Figueres itself isn't, for me, a particularly attractive city, but the DTM is very appealing--and I say that as someone who really doesn't care for Surrealism. The nearby jewelry collection, covered by the same ticket, is beautiful and can be seen in less than 30 minutes. The DTM can take a good bit of time if you want to see everything (definitely over 2 hours, maybe over 3). Although I don't think the DTM fully sells out, tickets are timed, and individual entry blocks can sell out. The museum does get some bus tours, and one busload might buy up a lot of tickets. Therefore, it would be a bit risky to head up to Figueres without having bought online tickets in advance. I think I bought mine just one day ahead, but that was in 2019, and my schedule was flexible. There are both fast trains (more expensive, especially if you buy the tickets late) and slow trains running from Girona to Figueres. They go to different Figueres stations. There's a city bus connecting the two stations and traveling within a few blocks of the DTM. However, in my experience, if the train is late, the bus doesn't wait, so plan ahead by either allowing for a walk (roughly 1 mile, I think, from the Figueres Vilafant station served by the fast trains) or carrying taxi telephone numbers in case there's not a taxi waiting when your train arrives.
Another possible side trip from Girona--this time by bus--is Besalu. Besalu has a medieval center that's fun to wander. It also has a very distinctive merchant's bridge.
If you wanted to push harder and had extra time, you could go beyond Figueres to Cadaques by bus. Cadaques is a very pretty, white cubic former fishing village (not tiny), dripping with bougainvillea. It's touristy now. Outside Cadaques is another Dali-related site. It's in Portlligat, and that is a ticket that definitely does need to be purchased well ahead of time. Capacity there is limited. I think the house is about a 15-minute walk from the bus station or a 20-minute walk from the port area. The bus route from Figueres to Cadaques is very scenic. Those buses depart from outside the Figueres train station (called simply "Figueres) used by the slow trains.