Campsites are available in both the State and the National Park.
Personally, I prefer the State Campground as each campsite loop has a bath house with hot showers and sinks in the rear of the building in which to wash dishes.
The ponies of Assateague are probably it's most famous residents. Legend has it that they are descended from horses that escaped a sinking Spanish Galleon just off the coast in precolonial times. More probably they are descended from livestock that was grazing on island in the late 18th Century.