Rent a kayak / canoe rental and cruise through the mangroves or head out into the bay where you could see dolphins and manatees or just chill on the beach one a nearby island. There is also a bike trail for mountain biking, cabins that you can rent for overnight camping, pavillions and bbq areas for daytime parties and a little protected beach to swim on. They also have a fishing pier there.
As you can see, there are plenty of activities for the whole family. For more information, you can check out the Oleta State Park website