as mentioned, there's dispersed camping in George Washington NF, but I'd also suggest some of the campgrounds there.  Most are not used that much, they don't offer electricity, some just have pit toilets so it's fairly rustic, but you can park and have a tent pad - you might like Elizabeth Furnace - pretty setting along passage creek - or if there are too many trout fishermen, head further south into Fort Valley and try Camp Roosevelt.  just an idea.  from both places you'll find some nice hiking.