Lots of good suggestions for sightseeing. There's a tourist "trolley" in Savannah that we enjoyed. In Charleston, don't miss the Battery (the old downtown by the water), and if you are at all interested in the Navy or military history, Patriot's Point is wonderful. Middleton Gardens and several of the plantations are great too. (We lived there for a year, but it was many, many years ago. :) )
We have camped at Oak Plantation CG and found it to be quite nice. Didn't go to James Island and noticed that the route in goes through some streets that I didn't think I'd have wanted to tow a big trailer through - but perhaps that's just me. Oak Plantation is a private CG, FHUs and elec-water hookups available. Some of the sites are a bit more spacious than others, but on grass so can be a bit muddy if the weather's wet.
Don't miss Savannah downtown - the trolley tour is great, you can walk some of it, etc. Very different from Charleston but both are lovely old towns & didn't suffer major damage during the "late unpleasantness" in the 1860s. :) (Thankfully!) Also worth seeing around Savannah is Ft. Pulaski.