Hunting Island State Park  (2555 Sea Island Pkwy., 866/345-7275, www.huntingisland.com , daily 6 a.m.–6 p.m., until 9 p.m. DST, $4 adults, $1.50 children, $25 campsites, $87–172 cabins) has 200 campsites on the north end of the island, with individual water and electric hookups. Most are available by reservation only, but 20 are available on a first-come, first-served basis.
On the south end the park has 15 two- or three-bedroom cabins for rent, fully heated and air-conditioned and equipped with TVs and kitchens. The cabins sometimes fill up a full year in advance, so book as early as you can. There’s a one-week minimum stay during the high season (Mar.–Nov.) and a two-night minimum at other times. Also be aware that checkout time at the cabins is a chipper 10 a.m., which is strictly enforced.
Another neat place to camp is Tuck in De Wood (22 Tuc In De Wood Lane, St. Helena, 843/838-2267, $25), a 74-site campground just past the Penn Center  on St. Helena Island.