Nobody has mentioned it yet, but James Island is fantastic. Great park, nice and quiet at night but only a few minutes from Charleston. Great restaurants and plenty of grocery shopping nearby. Prices are quite reasonable and the park has a lot of activities if you are there in season.
Its a relatively short drive to Folly Beach, which is a cool little beach town just south of town.
Sites are plenty spacious. Lots of hiker/biker trails to get exercise. Our kids LOVE the playground nearby, which is a short walk from the campground.
We've been going there for over 10 years and ALWAYS stay there. Mondo's Italian restaurant is one of our favorites. Amazing food and a very nice atmosphere. They have a little outdoor bar area in season. If you like military history you HAVE to go to Mt Pleasant and visit Patriots Point. While you are in Mt Pleasant, Page's Okra Grill is one of my favorite southern style restaurants. Great breakfast and dinner foods. Then you can scoot over to the beaches at Sullivans or Isle of Palms.
Beautiful area, you can't go wrong with just about any decision.