day trip from Barcelona

We visited Barcelona in September for the same amount of time. While there, we rented bikes and spent a couple hours on the bicycle beach trail (about 10 miles round trip). Great people watching and if you wear your swimsuits under your clothes you can stop for a swim somewhere along the way.

We also took a day long side trip with Spanish Trails, called "Everything Dali", which took us to Cadaques to see the Dali home and also to Figueres to see his museum. Although we loved it, would not recommend for kids, as Dali lived a pretty sordid life. If you go anyway, remember that you must have advance reservations for the house, they will not let you in onsite without them (the house is small and only a handful allowed in at a time). HOWEVER, the excellent Spanish Trails company offers lots of interesting tours, including beach and kayak adventures....check it out: Be sure you see the "all tours" tab because that shows kayak tours, beach etc.
Have fun!
https://spanish-trails.com/tours/

Caveat: I don't have children.

Girona is about an hour from Barcelona. It has a walkable wall and a lovely historic district, plus some sights that might appeal at least to the adults (a couple of historic churches and a good small museum). Probably affordable only if you buy your AVE ticket far in advance or settle for the much slower non-AVE train.

Cadaques can be done as a day-trip from Barcelona: train to Figueres (again, buy AVE tickets early or spend a lot of extra time on the train) then bus to Cadaques. At least part of the bus ride is very picturesque, but as a child, "picturesque" didn't mean much to me. I did not go to the Dali house, which is outside Cadaques (about 20 minutes on foot from the beach; don't know how long a walk from the bus station). I believe the Theatre and Museum in Figueres would be more likely to interest the children, but I don't know about its age-appropriateness. I haven't been there either. I think you usually need to buy (timed) tickets to the Figueres site early.

I know there's walking at Montserrat; perhaps there's enough altitude there that it won't be too hot.

I can't help with beaches, but one of our Catalunya residents will be able to assist, I'm sure.

I'm sure Rick warns about buying tickets in advance for a lot of the most popular sights in Barcelona. Believe him.

I feel like the better beaches are located outside of city. One is called Platja del Garraf, which is just a short 30 min train ride south of Barcelona. You will find only locals at this beach. There are also many good places to eat nearby. La Cúpula is one such place, it has commanding views of the Mediterranean and a pretty good Fideuà, which is like a Paella but with short noodles instead of rice.

Another beach town that I went to a lot is called Tossa de Mar, its located 100 km north of Barcelona on the Costa Brava. It takes about 1:20 hr to get there by Sarfa bus. While Tossa has this idyllic medieval Mediterranean setting, it can get quite packed during the summer.

Another potential day trip (with a beach) could be Tarragona, which is 1:15 hr south of Barcelona via train. Tarragona has some of the best Roman ruins in Spain, including a Roman amphitheater and Praetorium tower, which are designated as World Heritage Sites by UNESCO. They also have a great Roman history museum called Museu Nacional Arqueològic (MNAT), showcasing various treasures from antiquity. The twisting medieval center also makes for a nice place for walks and dining.

About 2 miles west of Tarragona, at Pont del Diable, there is a totally intact Roman Aqueduct that is worth a look too. You can actually walk over it like a bridge (if you dare). The surrounding forested area is great for some casual hiking too.

@julie713, when are you visiting exactly? also, what do they like?

We went to Montserrat which was beautiful and on another day to Figueres to the Dali museum which kids would probably find fun. Montserrat is in a beautiful spot where 'shortish hikes' are part of the deal.

How did you travel to Montserrat?