Savage Gulf is a hiker's paradise with trails criss-crossing a crow's foot-shaped canyon complete with stunning canyon views, waterfalls, and a smidgen of old-growth forest.
The canyon is managed by South Cumberland State Park. Don't bother with the state's website -- not much information, here. The Friends of South Cumberland's site is worth a visit, though: http://www.friendsofscsra.org/aboutthepark.htm. They have the best available trail map posted here. The trailheads typically have very nice topo maps available freely at the kiosk.
Stays in the backcountry require a permit, but it's free. You'll have to pick one up at one of the ranger stations, at Savage Falls Trailhead and Stone Door. Also, you should expect a sunset visit from a park official, checking for permits. Alcohol is not allowed at Tennessee State Parks and they will fine you.