Depends what part of the state you are in, but if you can get over toward Norris (right off I-75 north of Knoxville) the Museum of Appalachia is great. They have some original mountain rifles, gunmaking equipment, some of Hacker Martins' equipment and rifles, I think about 25 or more log buildings, and thousands of other items on display from the region, from the 18th through 20th centuries. Some great Native American artifacts and the big Virginia dagger shown in Madison Grant's book too (Knife "BK-1"). Food is pretty good too.
The Tennesee State Museum in Nashville used to have some nice things too - the silver mounted Baxter Bean pistols in particular.
I don't know what the status of Mansker's Station is at the moment - if the Museum there is open, they have Jud Brennan's copy of the Thomas Simpson/ Mansker rifle.
There are lots of others - Some of the guys who live down that way could probably give you better/ more tips.
Guy