I'm not sure if you already took the trip to Savannah. But just in case, I'd recommend Skidaway Island RV Park. It's quite near the Historic District to do some sightseeing. At the same time, it's far enough that you are able to escape the city life. It offers the amenities of a private campground down to full hookups with the breathtaking sceneries you'd usually get from state parks. Shady sites but the bugs can be quite a problem so make sure to bring some bug spray with you. Also, make sure to make a reservation before heading here since it's usually full.
Hope this helps.