Oak Plantation is nice but several miles southeast of town. Also out that way is Lake Aire Campground. It's OK but not as nice as Oak Plantation. Gives better discounts, though, e.g. Passport America.
Closest in and quite nice is the campground at the James Island County Park. It's very popular and I've never successed in getting a site there, though.
Google any of those names for more info or check a campground guide such as Trailer Life or Woodalls.