I was just there over the 4th of July.
I can't give many specifics, but...
If you're there in Mid-October, you'll likely be around peak fall color. It'll be hard to go wrong.
Chickamauga is heavily wooded and you should have some beautiful scenery in the park.
Likely cool air and morning fog coming off the Tennessee River (don't know that it works this way in Chatt, but seems like it ought to)- so perhaps chances of early morning shots of mist. Could make for some good moody architectural/city shots.
Good vistas from Lookout Mountain.
I came; I saw; I shot; I shared.