It depends what your kids want to do and how far you deem the surrounding area to be. Without driving off the island, there's beaches and water activities, hiking, biking, and some historical museums. There are of course many things to do in the Tampa/St Petersburg area, but it's a bit of a drive to get off the islands and into the cities—on the order of eight or ten miles.
You can get a campground map online
here (pdf file). Site 101 abuts a seawall, so you're on the water but not the beach.
It is a lovely park and campground, in my opinion. I camped there with some good friends maybe a decade ago and remember the times fondly.