Dalford and d-mo have nailed the recommendations. James Island is a short drive to Charleston and Folly Beach (and the Firefly vodka plantation). MB State Park is a slice of beach as it was before developers got a hold of Mother Nature.
I'm sure there are plenty of other places, notably RV "resorts," but if you want amenities (water/electric/sewer) served up in a campground under hardwoods and live oaks, you can't do any better than those two parks, IMHO.
Wright and Penny
2010 Tundra 4X4 5.7L V8
2014 Rockwood 2604WS
Life is a cruel teacher. She gives the test first; the lesson then follows.