Not a campground but....we overnighted at the Savannah Visitors Center in Feb. They have spots for rvs. No hookups but it is $10 per night, Sunday's are free if you leave before 9am Monday. I think I recall hearing you can stay for two nights. They have a couple of water spigots to fill jugs. An easy 10 min walk to the historic district. Some of the trolleys have a stop here if you don't feel like walking, just check their hours to make sure it fits your plans. It is adjacent to some college classroom buildings so there were patrols all night. About a dozen rigs there the night we stayed. We arrived around 9 on Sunday morning, there was plenty of parking. When we got back that night it was close to full. Very quiet, got a good nights sleep.
We had a blast walking around, did a couple of tours, ate some great food and hit the road the next morning. Our rv is 27' and we had plenty of room. The Visitors Center could give you length restrictions.