Fancy yourself a modern-day Robinson Crusoe? Pitch your tent at Cinnamon Bay, the only beach in the park with a public campground. Here you'll also find kayak rentals, a restaurant and...limited parking, so don't expect to drive up at noon and easily find a spot.
There is a privately run campground, at Maho Bay, which offers 114 tent cottages for those who don't want to really rough it, and studio apartments. Condition of these facilities are commensurate with their age, and you'll pay more than if you pitched a tent at Cinnamon Bay, but these are a tad more substantial.