River's End Campground is, probably, closest and easiest drive to the Savannah area you want to visit. It is out on Tybee Island. It is an easy bike ride or walk to the lighthouse and beach. The campground has made some improvements. Some sites have been spread out alittle. Electrical connections have also seen improvements. When we were there in May, the bathroom situation was still the worst I have ever seen. There are several rooms that contain a sink, toilet, and shower. Maybe 10 or 12 of these rooms serve the entire campground. The rooms are in a raised building and years of "smell" has accumulated under the damp floors. Also, if you are tent camping or have a unit with no bathroom, you are forced to wait to use a toilet while the rooms are occupied with people showering. Security was excellent. The campground is fairly quiet. We usually see many children but they are always well behaved. Despite the bathrooms, we still return each year.
Skidaway Island State Park is further south. It is coastal but doesn't have a beach. The campground is very shaded. Most sites are a pretty good distance from neighbors. You won't have cable or full hookups at Skidaway. Bathrooms are typical GA State Park (older, clean, good hot water...).
Both campgrounds are about the same distance from Savannah but I like the bike riding access to the small town of Tybee, the beach, and the drive in from Tybee much better than Skidaway.