I lived in 'em for about 7 years. There are some truly stunning places, and many are off the beaten path and harder to get to than places I've been in the Rockies. And some are on the beaten path, too.
The Joyce Kilmer Memorial Forest would be worth a stop, and if you are an avid hiker you can take it further and visit the Joyce Kilmer-Slickrock Wilderness, where you can find some of the biggest old-growth hardwood trees left in North America. The Memorial Forest loop trail is an easy, short hike that is fairly popular while the Wilderness trails are more challenging (but that means fewer people around, which I prefer).
These aren't the largest trees in the area but are pretty good examples of what you'd find (I don't know who anyone in the photos is; I just grabbed 'em off a google search):
The giant tulip poplars are still doing okay, but many of the giant hemlocks (and they are truly GIANT) have been killed by the hemlock wooly adelgid in recent years. I'm not sure how bad the damage is since I haven't been there in nearly 10 years but that's also a good reason to go see what you can while you can since it might continue getting worse.
The Cherohala Skyway is worth a drive (it's a very popular motorcycle route):
It's also #1 on this list of scenic drives in America: http://www.travelze....hes-in-america/
There's also the Pisgah National Forest in North Carolina.
It's got some interesting features, such as Looking Glass Rock:
There are more streams and waterfalls around than you can count, and good/scenic hikes can be had pretty much anywhere you pull over and explore on just about any road in the Smokies.
In ~7 years I only managed to scratch the surface of places to explore (and I was working full-time as a rafting and mountain biking guide when I lived there).
Oh, and if you're anywhere where you can see the Citico Creek wilderness area, keep your eyes peeled at night for UFO's (they are very common there). You can see some photos of them that a friend of mine took in the area in this thread: https://mycotopia.ne...e-2#entry368916
Stay the hell away from Gatlinburg in Summer unless you're into scenic traffic jams of countless RVs that take you to a kitschy, hillbilly version of Las Vegas.
And it's a great place for mushrooms (hunting for wild ones as well as eating your homegrown ones).