Hey, I've been living here in Knoxville for about ten years and have fished the smokies all ten of them.
Your best bet during the summer is to try anything with yellow. Yellow foam caddis (called a neversink caddis down here) will usually work 90% of the time. Greenie weenies, which imitate an inchworm, work real well as a nymph. When the water is low and the mountains are hot, terrestrials, like black ants work too. The hatches at night consist of sulphurs and yellow sally stoneflies, so again, a dry with yellow is highly recommended.
Really, fishing in the Smokies, due to so much stress, is extremely difficult for the beginner. You really HAVE to have good drift, presentation, and LOW profile. Trust me, this makes the world of difference. Pocket water fishing is the most productive.