I can only speak for the lower part of South Carolina, and I can't think of any place like that. Beach access is a well guarded commodity. Hunting Island state park outside of Beaufort, SC, is beautiful. The campground isn't real big, but it's on the ocean. The beach is good for walking except during high tide at full and new moons, when tides are most extreme. I've heard good things about Huntington park in Myrtle Beach but you sure have to hack your way thru some traffic and sprawl to get there.
The barrier islands below Savannah, Georgia are mostly inaccessible by road until you get further south.
Good luck on your trip. If you like nature walking stuff, look into Donnelly wildlife management area below Charleston, SC, right off US 17. I wouldn't be keen on going in there in a large Class A or with a big 5th wheel, it's all dirt roads. The bird watching is excellent, and if it's warm you'll see enough gators to make your skin crawl.