Question regarding visiting basalu, Paratallada and either cadaques or tossa del mar

I have been to Besalu and Cadaques and recommend both. Haven't seen the other two so can't comment on them. I used the lovely Girona as my base for seeing Besalu and Cadaques. It also has much of interest itself--walkable wall, large historic district, two cathedrals and a good museum. It makes a very nice change from the hectic nature of Barcelona (a city I love).

I'd suggest going straight to Girona on your arrival day. If you're flying out of Barcelona on May 12, you really should spend the night of May 11 in the city, which argues for putting your Barcelona time at the end of the trip. You certainly shouldn't waste time by checking into Barcelona hotels twice.

You can buy a last-minute ticket on the slow train at no price penalty and reach Girona in about 80 minutes. (Note that you may save money by purchasing a round-trip ticket rather than two one-ways.) It will be a pleasant place to walk around in a jetlagged fog. Spend at least 3 nights there; 4 would probably be better since the first day is pretty much lost, and I think you'll want time to see Girona itself. Girona is an affluent town, and hotels there are not especially cheap. If it's your first stop, you should make a hotel reservation ahead of time.

There's bus service to Besalu. The bus stop is on the main road. On the day I visited Besalu and then headed west, my bus departed at least 8 minutes early, so get back to the bus stop (opposite side of the road from inbound stop) well ahead of time.

For Cadaques I took the train to Figueres and then a bus. You probably want the slower train to Figueres because it stops at the station very near the bus station. The fast trains to Figueres use a different, less convenient, station. There's also bus service from Girona to Cadaques, which would be a viable option if the schedule works for you.

There's reasonable bus service from Girona to Tossa via Lloret del Mar.

Peratallada is going to be more of a challenge, because bus service to cover the last leg looks infrequent, no matter whether you're starting from Girona (closer) or Barcelona (farther). I'm not sure it's going to be a practical destination for you. I found this TripAdvisor thread from 2014 that may be helpful.

Not making a hotel reservation for Barcelona is really, really risky from the financial standpoint. I don't know what to tell you about last-minute hotel reservations if you decide to stay in one of the smaller places. These days everyone travels with a smartphone, so even the wing-it travelers (and I am one myself) virtually always reserve at least 24 hours ahead of time. If you don't do that, you will end up with what no one else wanted in terms of location and price-to-value ratio. If you have a loose budget, it may not be too big a risk.

There is a tour of smaller Catalan villages that may interest you. I haven't taken it, but at least one person has posted positive comments about it on this forum. I think (but am not sure) that the tour in question was Explore Catalunya's "Small-Group Medieval Villages Day-Trip", which runs from Barcelona. When time is short, it's my opinion that tours like that can be worth the money. It's very difficult to visit two small, isolated towns in one day, much less three or four, if you're limited to trains and public buses.

I am the one who took the day tour acraven mentions at the end of the message, and I found it excellent. We met in downtown Barcelona, then to Besalu, then to Rupit (where we shared a very good group meal, cost not included in the tour), then to Tavertet. The tour guide, Josep, was local to that area and really top notch. I remember that the traffic in and out of Barcelona was heavy and slow, and I was happy that I was not driving myself.

The only one I've visited is Cadaques, but I have to just say that it's one of the most beautiful places I've been.

I rent a car for a day to go north of Barcelona.
We went to Tossa de mar and Perratallada.
Tossa de mar is nice but not necessarily a must.
But we found Perratallada very charming. It is a very small medieval village that will not take more than 2 hours of your time, but if can see it, go ahead, especially since you seem to be a fan of medieval time and villages(we definitly are as well)
Claude