From your description Bob, Hunting Island might well be the Park you visited. There is a lighthouse and the perimeter sites on the ocean are subject to severe beach erosion. Unlike our NC Outer Banks, there were no sand dunes to serve as a barrier from the sea. Still, we enjoy visiting there - beautiful old live oaks scattered througout the park, great bike trails from the campground to the lighthouse through a maritime forest and the sand is packed hard enough to ride along the shore (not possible on NC's beaches). We've got to get you out of them thar hills for a downeast visit one of these days.
Oh, I go to the coast for at least two vacations per year. This year we went to Juniper Springs in Florida (not the beach, but a freshwater spring, and we spent time on the ocean), and we went to Huntington Beach State Park south of Myrtle Beach (which is my favorite coastal park in SC). And in April we're taking two weeks off to hit the Florida Keys! Neither of us has ever been to the Keys, so we're hoping to have a great time down there.
In fact, here's our campsite at Huntington Beach State Park from just a few weeks ago (September).