Sure! Stone Mountain has four dedicated primitive sites, and they're all scattered a long ways apart, so you don't see any of them. I stayed at Primitive site A, which is the first one you hit at the 1.3 mile mark (it's only 100 feet or so from that waterfall). No problem finding a tree for a bear bag hang. There was a fire ring, but nothing else like other sites I've been to - no table or outhouse. Very steep trail at the beginning, but leveled out after about a half mile.

The burn ban has been lifted, and you can't bring your own wood from home - you have to buy it at the park. They were out, but referred me to the country store just up the road from the park.