When I lived in ky I would back pack the gorge a lot. Lots of great trails and camping. Auxier ridge is a great one to start on. Indian stair case and cloudsplitter are great views, but can get busy with people. My favorite trail was swift camp, as it always seemed to have less people and it was a great workout. The rough trail is also a nice long hike, and connects to swift camp.
I would recommend getting some good maps, as there are a lot of off trail systems that can get confusing if you're not use to it.