Lookout Mountain
I don't know much about firearms related in Chatanooga, but I have been there a couple of times. Two tourist things: Lookout Mountain, and a railroad museum. Lookout mountain has several historical attractions. One is a tour thru the caves within the mountain. At the end of the caves is, Ruby Falls, a waterfall within the mountain. Very impressive and a nice tour. There are other things, but one of interest is the show about a Civil War battle of Seminary Ridge where Gen. Douglas MacArthur's father, Arthur MacArthur, won the Medal of Honor.
The train museum is very pretty and well set up for a look-see (mostly free). To get around the town, as I recall, is a trolley setup and very convenient. The whole city is on human scale; one of my favorite places. My wife like the shopping centers near the city. Have a nice trip.