Gatlinburg/Pigeon Forge is not a great place for beers but it's getting a little better. The only brewery I'm aware of in the Gatlinburg area is Smokey Mountain Brewery. I really like their porter. There other beers are OK but nothing special IMO.
As for local beers, any of the saisons by Blackberry Farms are outstanding. Yazoo has a smoked porter (Sue) and a Flanders red that I like. Wiseacre also has some nice ones.
If you can get to Knoxville, Crafty Bastard, Schultz Brau, and Alliance breweries are good. And if you head just a little east there's Asheville.