Bass Pro out by the interstate. duh!
The Big South Fork (KY) is like the Smokies in reverse AND theres rarely anyone there. Beautiful place.
Historic Ducktown/Copperhill
Lookout Mtn/Chattanooga
Rockhounding in the Spruce Pine NC area.
Knoxville Expo Center has a decent flea market a weekend or 2 a month. they have a website you can check dates.
Knoxville Zoo isn't bad for a small town zoo.
Personally, I avoid that tourist trap of pigeon forge/gatlinburg like the plague. And if you don't like going 5mph all day with frequent stops, don't do Cades Cove. Get out and take some of the small trails in the Smokies, especially on the 'other side'. I am a local if you want to bounce anything off me via PM.