Here is one place to look. http://www.state.tn.us/safety/handgun/handguntca.htm
There basically 5 places prohibited to carry by law in TN.
39-17-1305 Places where alcohol is served for onsite conumption.
39-17-1306 In a room where a judicial proceeding is taking place.
39-17-1309 On school grounds.
They can be left in your car 39-17-1309(c)(1) [Second half] or left on your person in your car if you are simply picking up or dropping off someone as long as you dont' get out of the car or handle the weapon. 39-17-1310
39-17-1311 Public parks, playgrounds, civic centers and other public recreational buildings and grounds.
There is a list of exemptions (including in your car while dropping off and picking up) under subpart (b)(1)(G)
39-17-1359 Any place with a properly posted sign that states the prohibation of the carry of weapons on that property.
As you already know...most weapons laws are covered under Title 39, Chapter 17, Part 13 (39-17-13xx) in the T.C.A. there are some hunting laws that address weapons under Title 70.