I'm guessing your family group includes a wide range of ages, including a good number of seniors, with some of the latter perhaps having mobility challenges. Lots of picturesque destinations are hilly.
I liked both Girona and Cadaques, but there's a lot more to see in Girona. Cadaques is primarily a gorgeous white former fishing village (now very touristy) dripping with bougainvillea. There's a Dali site outside of town, and the last part of the trip (which must be made by road) is very scenic. Girona has a medieval district with parts of the (walkable) wall remaining, two interesting churches, a Jewish Museum and a nice, not-too-large art museum. I believe Girona also has some seriously good restaurants (not that those in Cadaques are bad).
In my view the only reason to go to Figueres is to see the Dali Theatre-Museum and the co-managed jewelry collection. I enjoyed both a lot, but Figueres-the-town isn't particularly attractive, compared to other options. Those interested in neither art nor over-the-top jewelry probably wouldn't find much to do there.
All of the above are north of Barcelona, so they're quicker to visit from Barcelona than from Sitges. I think most folks go to Montserrat by train and then some sort of cable car or lift. If you were staying in Sitges, you'd need to get to Barcelona to start your trek to Montserrat by train.
Another option north of Barcelona (actually west of Girona--which also makes an excellent base for side-trips to Figueres and Cadaques) is Besalu, a small town with a medieval center and a fortified bridge. There's bus service from Girona and I think also from Barcelona. One of our other posters has written about a nice one-day bus tour he took to medieval villages in Catalunya, one of which was Besalu. You might take a look at the description of that tour and consider whether at least some of your family would enjoy doing something like that on a private tour. It seems the tour is conducted by a company called "Explore Catalunya", but I don't see it listed on that company's website; perhaps that's just because of COVID-19. This is a situation in which having your own transportation would be fabulous; you could visit multiple small towns in a single day with ease. Via public transportation you probably would only be able to get to one per day. I'd be shocked if the company wasn't willing to run a private tour for whatever part of your group was interested.
South of Sitges you have the coastal city of Tarragona, which has some Roman ruins (which I have not seen). Outside Tarragona is the smaller town of Reus, birthplace of the famous Catalan architect Antoni Gaudi. There are no Gaudi-designed buildings in Reus, but there is some lovely modernista architecture by others. Two of those buildings can be toured. If your group includes one or more modernista-architecture nuts, I definitely recommend Reus for them.
Zaragoza is about 1 hr. 45 min. SE of Barcelona by fast train (an hour or so longer by bus). It has a very nice historic center and a Moorish palace that has been refurbished and can be toured. It would take longer to get to Zaragoza from Sitges, because you'd first have to get to Barcelona. I should also mention that Zaragoza is likely to be seriously hot in June.
There are fabulous day-trip options from Madrid, and you're already familiar with the charms of Andalucia. However, June is not the best time of year to visit central and southern Spain because of the heat. If you're not lucky with the weather, it might be hard on any older people in your group. Arranging private bus transportation would reduce the time spent standing around waiting on scheduled service and maximize the time spent in an air-conditioned environment, but the fact is that the AVE trains are the fastest way to cover long distances, such as along the Madrid-Cordoba-Seville line.
