Alum Cave Trail is my favorite in the smokies. A few geological features, a few stream crossings in the first mile. And the fews near the summit of Mt. LeConte are incredible. Especially this time of year. 10 mile out and back, but you don't have to do all it.
You could also hike to Charlies Bunion, which is on the AT. Great 360 degree views. 8 miles out and back.
You can hike 2.6 miles to Rainbow Falls via the trail of the same name.
Also, check out this website: http://www.hikinginthesmokys.com/