Hunting Island SP, which is on the Atlantic Ocean outside of Beaufort, SC is fabulous. It's a SP, so $30/night. Water/electric only, but 2 dump stations within the park. As the crow flies, about a mile from Parris Island, but on the road, about 10 miles.
You may have trouble finding a spot this late, at least one that is close to the water, but even the ones in the very back, you are less than a 5 minute walk to the sand. This puts you closer to the playground. Bikes are plentiful, kids are plentiful, lots of trails, some good kids programs, but you have to drive out to the park office at the pier (about 3-4 miles away).
It is about 1/2 way between Charleston and Savannah, so a great place to do day-trips from.
