Okay, so you are not supposed to camp on the AT in the Smokys. You can generally camp at a shelter if you are a thru hiker (start and end 50 miles outside of the park) and the shelter is full. The only legal place you can camp is at a former shelter site, near Shuckstack mountain. I think it is still shown on park maps as being the Birch Spring shelter.
If you want to do some illegal camping, remember to set up late (like after 7) after the day hikers have gone home and pack up early (before 7) before they come out again. Be gentle. The no camping provision is in place to keep the AT looking good. Don't screw it up. The Mt. Cammerer fire tower doesn't have any where convenient to throw up a tent, tarp, or hammock, but you can easily sleep inside the tower to get a nice sunrise. Just east of Tricorner shelfter is a former landing zone for choppers, I believe. Regardless, it also makes a good place to stop, particularly if you arrive at Tricorner and find a zoo (as in any time in the month of April). There are other great spots, but you'll have to find those for yourself.