We go for daytrips, mostly (2 hours away) but we've also enjoyed our timeshare stays at the
Fairfield Smoky Mountains Resort in Sevierville, TN. This is just on the far side of Pigeon Forge. Gorgeous 1BR, 2BR, 3BR and 4BR condos! Heated indoor pool, fitness center, game room, gathering room, outdoor pool, kiddie pool & hot tub. Very nice resort set a half mile back from the strip, so peaceful. It's very new, with its second phase still under construction but unobtrusive.
Sevierville is easier to reach from I-40, before you get into the heavy traffic of PF and Gatlinburg. We know the back roads to get to Dollywood from there without spending much time on the strip. Wherever you stay, call ahead and ask them to mail you an area road map (may be found in most of the free tourist magazines). This will save you a lot of time if you will be there during a busy season.
There are several more timeshare resorts which may suit your needs. Examples might include Laurel Crest Resort, Sunrise Ridge Resort, Sunterra Bent Creek Golf Village, Treetops Resort and Westgate Smoky Mountains Resort. None of these are in town and all would require a drive to reach the attractions. However, this is usually only really a problem if you are driving during a busy season weekend. Midweek, it's really not that bad, IMHO. These resorts may offer a few more amenities than most hotels. Weekly rentals from owners may be found in the
TUG Classifieds - most people list Gatlinburg area rentals in the "Eastern U.S." section, sometimes in "Central U.S." HTH!