First time to Spain

I don't currently have the Spain Rick Steves Guidebook, but he details how to get to Segovia from Madrid. Its easy. You do not need to book tickets in advance. There are two ways to get to Segovia. One is to take a train to the Segovia train station and then take a bus that is typically waiting or will arrive soon, to city center. The other is to take a bus from Madrid. I believe the bus is cheaper by a bit, and goes directly to Segovia city center. I believe the train is faster.

I don't like to recommend Toledo as a day trip because it takes a few days to explore, but I feel like it is pretty high on the list of "must sees", and the kiddos may like the vibe (castles, knights, swords) It is an amazing and beautiful city with a lot to see (cathedral and castle) and is easy to get to from Madrid. It is about a half hour from the Atocha train station. These train tickets can sell out, to be safe, you could purchase your tickets a few days in advance. You would likely want to take a taxi from the Toledo train station to city center. You could ask the driver to take a slight detour to the viewpoint of Toledo from across the river prior to getting up to city center.

I didn't go to a beach town near Barcelona. There are beaches IN Barcelona in the Barceloneta area. We collected sea glass (which was legal at least when we were there). A day trip to Montserrat up at higher elevation should be cooler.

EDITED TO ADD: The kids could really love Park Guell in Barcelona. I would try to enter right when it opens. I would think they'd love a walk down Manzana De La Discordia (The Block of Discard). Some of the buildings are quite unusual and beautiful.

jules has given you some pretty solid answers.

1) I took the train from Chamartin (booked via Renfe) and then the waiting bus (paid on board). I stayed several nights, but the transportation works the same either way.
3) Montserrat might be an option in Barcelona. It’s on the mountain and definitely cooler.

Kids might like the maritime museum in Barcelona - sort of bottom of the Ramblas.

The kids might like walking the walls in Avila. We, seniors, did too! They might also enjoy the cable car from Barcelona to Montserrat.

Your kids would probably enjoy a flamenco show. I know southern Spain is more known for flamenco, but I've seen great performances in both Madrid and Barcelona. Yes, the places were touristy, but the dancers and musicians have always been awesome.

You don't have to leave Barcelona to reach the beach. FYI, nudity is allowed, and I have always seen some during the summertime, mostly topless women sunbathing. You might have a conversation with the kids before visiting the beach.

Tarragona is an easy daytrip from Barcelona. The Roman ruins are interesting, and they are even more impressive if someone has never seen an ancient amphitheater before.

Barcelona has a beach. With as little time as you have I wouldn’t use it going to a separate beach town.

My opinion regarding flamenco is 5 minutes of it is 4 too many. I personally feel no child would want to sit through an hour of it. Show them some videos to gauge if they may like it or not, if you think that’s something you might want to do.

My children were slightly older than 10, 11 when we took them all over Spain. Neither wanted to enter a museum, but both enjoyed the old castles, churches, and Roman ruins. Try to include some of their likes in your plan.

Most of Spain is hot in late June, so plan your daily activities to the extent possible, to avoid being outdoors in minimally shaded area during the hottest part of the day.

1. Segovia would be a nice day trip, pretty impressive with the viaduct, a nice plaza in front of the cathedral, then a pretty decent castle tour with a great view at the top of the town. Tickets can be had at the Charmartin train station, for that many people though, either go to a counter, or use the Renfe app to book. Spain requires you provide passport and other info on each passenger, so the machines take too much time, on the app, you can set each person up as a traveler, making buying tickets easy. If the app gives you problems, then maybe go to Trainline.com

Madrid and kids? If they are soccer fans, you can tour the Real Madrid stadium. The bullfighting ring has a museum, but I suppose it might be a bit gory in places, but mostly regalia and history, with a chance to walk in a bullring. There are a number of parks and gardens, some with some activities. If they are a bit adventurous, there are lots of weird things to eat, expanding their palette might be worth some time.

For Barcelona, side trips that are popular are Figueres for the Salvador Dali museum and theater, they may not be art fans, but Dali is his own type of entertainment. The other is the Montserrat Monastery. In a pretty dramatic mountainside setting, likely cooler than the city, something I think the whale family would like.

For restaurants, unless it is a high profile place, you can usually get in by going early, which for Spain is like 8 or 9 in the evening. Any place that is open earlier, you can just usually walk right in, but realize that it is a bit tougher with 6. If there is a specific place you want to go, then best to make reservations. Many places have online systems.

As for where to eat, In Madrid, I usually just do Raciones, kind of like tapas but like a shared appetizer. Lots of variety, I could go on and on about my favorite places, but go to YouTube, look up a channel called Spain Revealed, James has loads of tapas recommendations and restaurant recs for Madrid, plus a few for Barcelona. Paella might be fun in Madrid, several good places, in barcelona, they may not refer to it as paella, but still good rice dishes. Of course in Madrid, and certainly Segovia, roast suckling pig is popular.

We were very impressed by the National Archeological Museum in Madrid. It's close to El Retiro Park, which the kids might enjoy.
In Barcelona, check this schedule to see if you can watch the Castellers: https://castellscat.cat/en/schedule?a=2025&m=07&p=189
You could also look at the Castellers websites to see about attending a practice session to watch or participate in!

Our favorite town was Toledo, stayed next to the El Greco Museum in an apartment for $80 for 2 bedrooms, on a park, in the lovely old town. El Greco Hotel is very nice our friend stayed there. Walk to everything. Worth 2-3 nights for sure.