We haven't camped in Georgia actually, but my favorite State Park is about 30 minutes from our house .... Amicalola State park. There is camping there but I've never seen the campground. We take out of town visitors there to see the Falls, one of the tallest (736 feet) in the Southeast. It's particularly beautiful in the fall .... see link from our travel channel .... http://www.youtube.com/watch?v=pjMMZTI_AR8
There are lots of hiking trails as well as trails and viewing points to see the falls from various levels. At the top of the falls, you can actually look right over the top of the falls. There is a really nice lodge at the top with a spectacular view and nice restaurant also. All the footage in the video was shot in the park.
If you want to see what the falls look like in the summer and what nearby Lake Lanier looks like, you can view another video made when some friends visited back in 2011 ..... http://www.youtube.com/watch?v=dOmQy5F1HcE
There are also lots of Corps of Engineer campgrounds around Lake Lanier that look nice from the lake, but again, we've never actually camped there. There are lots of campgrounds with beautiful natural surroundings spread all throughout the north Georgia Mountains. The beginning of the Appalachian Trail is found in this area also.
Let us know if you ever plan to get down this way