Barcelona side trips-Pyrenees, balearics, France, or something else?

I should add that I much prefer a place accessible through public transit, but not necessarily ruling out renting a car either.

My two cents for hiking in nature:

Vall de Núria: reachable by train, 2h from Barcelona. Actually a train and then a rack train
Parc Nacional d'Aigüestortes i Estany de Sant Maurici: by car, some 4 hours from Barcelona

Tossa de mar is an interesting, historic town 100 kilometers north of Barcelona on the Costa Brava.

Good idea making the escapade from Barcelona for a few days, June/July is going to be hot, humid, and crowded in the city... yuck lol!

In Spain we have very good public transportation, however this only really connects metropolitan/urban areas, to access the mountains/countryside/villages a car is really the only practical way to go.

One exception as mentioned above is the to take the regional R3 train up to the Pyrenees mountain town of Ribes de Freser for a few days. From there you can take the rack railway up to smaller medieval stone village of Queralbs and then on to the Vall de Núria sanctuary for some amazing hiking. This is the train line https://en.wikipedia.org/wiki/R3_(Rodalies_de_Catalunya)
then switch to this one at Ribes de Freser to up the mountains
https://en.wikipedia.org/wiki/Vall_de_N%C3%BAria_Rack_Railway

If you have a car that opens a lot more options. There are plenty of fun activities (like snorkeling, sea kayaking) and excellent beaches along the Costa Brava. When I was a young boy my family would spend our summer holidays at Tossa de Mar. Alternatively Calella de Palafrugell offers a more low key beach destination. One can hike between the Costa Brava towns along the coastal Camino de Ronda. Be warned it will be very busy with foreign tourists this time of year.

Alternatively, inland in the Pyrenees foothills there are plenty of charming medieval towns and villages that are popular with local Catalan families on their summer holidays. Rupit (my favorite), Besalu, Camprodon, and Castellfollit de la Roca come to mind, with good hiking nearby. For Rupit I recommend staying in Hostal Estrella, very charming and rustic, nearby are municipal pools, perfect to cool off after a day hiking.

Further afield you can consider going deeper into the Pyrenees, using the mountain town Vielha as a home base, very interesting place, the capital of a micro autonomous community called Aran with their own language and culture. Here's a good article from the BBC about it if interested about Aran's little known story - https://www.bbc.com/travel/article/20220117-aranese-spains-little-known-language

Thank you all for the suggestions!