I've seen some decent "wallering" down there on the nature trail, but nothing great.
Others here have done some adventure trad, i.e. John Aragon and Don McGlone.
Certainly!! In Breaks Interstate Park if you drive past the lodge until the road ends at an oval turnaround/parking/overlook area, there is a trail on your left that goes down the hill a bit. The first rock you come to has a nice 5.6 crack. I've done a variation that breaks left at about 20 ft and traverses to another crack that goes about 5.9. Belay from the overlook railing. Further down the hill on the right you will come to a nice concentration (10 or so) of sport routes. The easiest seemed about 5.9 or so - several were harder. If you can find the right pulloff (before the steep river access road) you can walk along the railroad tracks for a mile or two (and through a tunnel) and find lots of cliff with adventure trad potential. I've done several multi-pitch routes with decent pro and dirty and loose rock. If you like to boulder, there's all kinds of potential along the river in an amazing setting. The Russell Fork is a very beautiful class 4-5 whitewater river with boulders ALL OVER the place. I've never been there with a pad, but have been trying to drum up some interest for some time now. Route development didn't seem to be an issue and was actually ENCOURAGED by the park service person I have spoke with. Being in Virginia they seem to recognize the assets they have and try to promote it instead of trying to shut down anything they see people having fun at. But I degress - Enjoy!
Shedding off one more layer of skin
Keeping one step ahead of the persecutor within
If you are going to be there anyway it would diffently be worth checking out. ask any ranger for direction. like Don said they wnat people to climb there. However, they will busted your ass double quick for drinking, littering or any other stupid thing you should not be doing anyway.