The Obed is an hour west of Knoxville, which is a fantastic area. There's Foster Falls in Jasper TN with an impressive amount of sport routes with a fairly easy approach. Both of these are Cumberland plateau sandstone.
Just west of Nashville proper in Clarksville is Kings Bluff, a limestone crag with numerous fairly generic climbs but the approach is a breeze and the routes have markers. Kings is an absolute inferno on a hot autumn day though.