There's a ton of stuff to do in and around the TN/NC border in the Great Smoky Mountains, both in and outside of the national park. Excellent trout fishing with a good outfitter in Townsend TN, a small town with a few restaurants and grocery, etc near the entrance to the National Park and the road up to Cades Cove campground, which is also a fav to many, especially in the fall. Lots of hiking trails with amazing views, biking ops, history, just all sorts of things. Also two national forests near the Smokies in NC, too; the Nantahala and Pisgah Nat'l Forests, with the Chatahoochee and Cherokee Nat'l Forests nearby in GA and TN/NC. You'll have no problem cramming as much or little as you want into 2-3 weeks. Personally, I'd steer clear of Gatlinburg and Pigeon Forge, unless you want to see mini-versions of Las Vegas and huge tourist traps.
Asheville NC, too, is chock full of interesting things from the grand Biltmore Estate--where the last Overland Expo East was held last Sept--to tons of restaurants and shops and museums.
If you're going all the way to the coast, there's enough there, too, to keep you busy the whole trip, from Charleston to Myrtle Beach to Nags Head. An awful lot will depend on if you're traveling solo or have family/friends along and what their interests are and what percentage of camping you want to do and what percentage of small town exploring. If traveling solo, I usually plan to only do a hundred miles or so a day, often less, and take my time exploring both small towns and camping.
You've got almost a year to plan, and I'm sure it will all settle down into a doable, fun, trip. I'd keep some of the exploring to new stuff and not only what others have recommended.
