Damn, I don't really know of any places in that area. Around my area (Central Ohio), I know that Hocking Hills is a nice area. There's kayaking/canoeing on the Hocking River (nothing all that intense), Old Man's Cave, lots of nice hiking trails, ect. If you're looking for something more rustic/not as popular, Tar Hollow is nearby and very similar to Hocking Hills, and you can actually easily access Hocking Hills from there, but less crowded.
In Western Kentucky there's Columbus Beaumont State Park. I don't know about hiking or other opportunities there, but I know there are really breathtaking views of the Mississippi River, as the campsites are situated on bluffs overlooking the river. It's very nice.