Where to shoot depends some on where you live and how far you want to drive, but ORSA is the best place around. You can get some info on it here:
orsaonline.org The 200 yard range and several other ranges are always open to members. The 1000 yard range is only open during competitions and certain practice times.
If you want me to sponsor your membership application to ORSA just send me a PM.
Tactical Advantage Corp (formerly Coal Creek Armory) has a pretty nice indoor range (pistol calibers only). You'll have a long wait for a shooting lane on the weekends though.
Gunny's in Maryville has a decent indoor range. And they let you shoot some rifle calibers, as long as you aren't shooting steel core ammo. Plus I've never had to wait for a lane at Gunny's. While I'm over that way I usually swing by Bill's Outpost in Alcoa, currently my favorite gun store in the area.
As for where to take your CCW class, I know people that have taken the class at ORSA (you don't have to be a member to take it there), Coal Creek and Gunny's. They all seem about the same. I took the class at Coal Creek, but that instructor isn't there anymore so I don't know much about the classes Tactical Advantage offers now, but I doubt they would be any different. You basically sit all Saturday in a room going over what will be on the test. Then you take a written test, and a shooting test. Then you go get fingerprinted somewhere, and go to the DMV to get your picture taken, and wait on the permit to come in the mail.