We prefer state and COE parks and have visited quite a few in the area.
Lake Lanier is south of Gainsville and has several COE parks... which offer a really nice discount (50%) to senior pass holders (if you qualify).
I'm surprised no one has mentioned Unicoi (Helen, GA) & Vogel (Blairsville, GA) State Parks. Both are really nice. There are several private parks in the area also.
I don't think you would like driving the MH up to the Amicalola Falls SP campground... it's a bit steap and the sites are small. The park is great and worth the trip... just not in the MH.
Enjoy your stay in our great state... We're traveling to yours this week. ;)
Happy Camping!
John.