As a bonded LEO, you can carry anywhere in the US per HR 214. Now that dont mean to try it in NYC, but TN is LE and CCW friendly. Just use your head and dont carry it anyplace you obviously shouldnt(airports, consuming alcohol, etc) and besides, if no one sees it, its never a concern.
HOWEVER, do know that the National Park System does not recognize HR 214 OR TN state law and may charge you if you carry inside the Park. Usually its the Ahole young ones. (all of this paragraph is per an ex SMNP ranger). According to my bud, it has been taken to court twice in the last 10 years and the LE officer has won both times (TN officer inside Park). Some arrogant types learn slow.
Theres tons of stuff to do (hiking, rafting, copter rides, bungee, Dollywood, etc), but I cant put my finger on anything specifically shooting related. Next gunshow that I'm aware of in east TN isnt until 8/11-12.