Not Eastern Tennessee, but close...
I stayed at Dragon's Rest (www.dragonsrestcabins.com
) in Robbinsville a few years ago. Pulled in there on a whim (and without a reservation) to hunker down during a massive thunderstorm and got a small one-room cabin for the night. They have covered motorcycle parking with hoses, etc. where you can clean the crud off your bike, which I considered a nice bonus after building up a rather extensive insect collection on the beemer all day and riding through the afternoon storm on muddy roads. Nothing fancy, but very reasonable price (~$75/night IIRC) and close to many "destination" roads, e.g., US-129, Cherohala Skyway, etc.
Several more cabin rentals near Robbinsville too, but I have no first-hand experience with those. If you're looking for something further east, I'd suggest staying near Watauga Lake--beautiful area!
Of course, there are also beaucoup cabin rentals near the Smoky Mountain (Gatlinburg and Pigeon Forge) if that's the sort of thing you're looking for. Wife and I have rented cabins from Aunt Bug's in Pigeon Forge (www.auntbugs.com
) several times over the past decade. Although their office is in town, they've got a wide selection of cabins scattered throughout the surrounding area. We've always been happy with their cabins and overall service.