When we were living in San Juan, lots of kids in the neighborhood would find all kinds of interesting things to do in Old San Juan. Don't forget to try the Piragua (shaved ice) and the helado (ice cream) from the vendors! Coco and Parcha are my favorites!
There are lots of parks, and although they may be a bit young, the forts are always fun. Lots of school groups there and steady wind for kite flying. There's a children's museum in Old San Juan as well. Old San Juan is a really fun city for all ages.
In Bayamón there is a manatee rescue facility that has visiting hours. Homeschoolers went there a lot.
I lived there before the hurricane, so you might want to see if there are any changes to the visitation hours or schedule.