Trail trailhead then hike to LeConte and down Trillium Gap past Grotto Falls back into Gatlinburg. Maybe 12 miles total...long day but worth it.
Nother good hike is from the visitor center up to the Ober Gatlinburg tram terminal and back. Maybe 4+ miles each way.
Watch out for bears, copperheads and water moccasins. Tons of each in the park.