Cumberland Island offers close campsites to the ferry (Sea Camp) + 3 backcountry campsites.
Cumberland Island is surreal. Although a ferry ride is required from the mainland, it is well worth it. Hopping off of the short boat ride, you can feel that this place is something special. Live Oaks covered in Spanish Moss cover the entire island. Only a certain number of people are allowed on the National Seashore at a time so you never have to worry about overpopulated trails or campsites. The only vehicles allowed on the island are the government owned ones.
There is a trail the crosses the island to the eastern shore right at the boat landing (which is southwest), or you can continue further north up the island. To properly explore the island, a 4 nighter would be most appropriate, the island is huge!
When backpacking the island, take the ferry across Fancy Bluff Creek. Once you've made it to the landing, check in at Sea Camp, where you can be assigned other campsites around the island ranging from 5.5 to 10.5 miles from Sea Camp. The most convenient trail to the backcountry sites is the Parallel Trail.
The foliage is unreal and seeing wild horses is a magical experience. The trails are all very flat, so the miles are pretty easy. Dispersed throughout the island are ruins left over from when the Carnegie family owned the island and lived on it.
I highly recommend everyone in the US makes the trip to Cumberland at least once in their life. Make your campground reservations here.