For lack of a better name, the MoA group is a group of guys I play with which includes Bob Bryant, author of Might of Arms. Mostly historical, our games include 15mm MoA (obviously) and variants, 15mm Battlefront WW2 and Flames of War, 25mm TSATF Boer War, Piquet: Field of Battle, Check Your Six, home rules, board games and others. We mostly play on Friday nights at somebody's house.
Yankee Peddler: Probably the oldest group around, having been around over twenty years. They are a dues-based club ($20/mo, I believe, although it used to be negotiable based on how often you play down there) as they have their own gaming space in the rear of a strip mall. There is a large 8'x12' or so table, and a smaller one. They play a lot of Warhammer, and typically run historical games every other weekend. They often play home-brew Colonial rules, as well as 15mm Johnny Reb 2, 25mm AWI and Napoleonics (incl. Egypt), 15mm Limeys and Slimeys and others. There are also some RPG games. Games are usually run on Saturday mornings. I was a member for a while, but as my kids got older, I just couldn't make Saturday mornings anymore.
The local Hobbytown USA has started regular miniature gaming, both Games Workshop and various historical games such as Hail Caesar, Black Powder, Flames of War, Bolt Action, and Force on Force. The guy to contact is about this is Ed Bardill at 387-1514. Organized Play carries Games Workshop figures and runs a couple of leagues. They also have open gaming.
They don't mention it on their website, but Sci-Fi City opened up a store in East Town Mall or whatever it is called now (Knoxville Center Mall? East Knoxville near I-40/I-640 intersection). The rumor I've heard is a guy who ran WarMachine out at the Barony is running it at Sci-Fi City now.
You can also check out KnoxGamers for the local gaming scene, although there is more focus on RPGs there. There is also TN Wargamers and the Atomic City Gaming League for gaming in Oak Ridge.
Also, the Tenn Soldiers site. I don't know much about these guys, other than they're somewhat related to Yankee Peddler and appear to be GW-focused.