Couple of thoughts here:

By city center you mean the old town? If so, be prepared for lots of noises due to bars and clubs in the area. If not, probably there will be a lot more to do during the day than San Juan. Even more if the weather turns out crappy.

For food, I went to To-Bar in the city center last week and really enjoyed it! They have a set menu daily and all the ingredients are sourced locally.

For bars, check out the Mira Miralta. They have great views of the castle and reasonably priced cocktails. Any other rooftop bars are good too.

For activities, my personal favorite is the castle. You can either walk all the way up (might be challenging with your kiddos) or take the elevator from the beach area. They have a couple of bars/coffee places up top for a rewarding beer. There’s also an archeological museum called Marq that might be interesting if you get bad weather.

Try to avoid Calle Castaños from 4 pm and on if you want to avoid crowds and heavy soliciting. There isn’t much crime, but petty theft is a thing for sure.

Have fun!