When we want to visit Savannah, we camp at Rivers End on Tybee Island. It's a short walk to the beach. It's a city owned campground, sites very close to each other, most have at least water & electric, wifi, cable tv. It's on a side street, and some of the sites are right on the street. Bathrooms are in a couple prefab units, each room separate with a toilet, sink, and shower. Probably not what you're looking for, but it's close to the beach, and 10 miles or so into Savannah.