Your handgun permit was issued by the state, and only the state may make laws pertaining to it.
According to the laws of the state, businesses and other establishments, as well as individuals may ban you from the premises by announcing "no guns allowed, or by erecting a sign with proper wording. You should not carry into those places.
There is also a list of places that are off limits by the state: schools, courthouses, places where alcohol is served, and government owned or operated places for the purpose of entertainment.
But as far as a county or city making its own rules for the carrying of handguns, that is not done in Tennessee. If you have proof it's being done, you probably have grounds for a lawsuit.
All of this should have been explained when you took the mandatory 8 hour class required for obtaining a permit.
And of course, anytime you are unsure of the law and off-limit places, it's always wize to read the laws governing the carrying of firearms in Tennessee.
Hope this helps. Good luck.