Blue Ridge Parkway is much better IMHO. Of course, I live about 10 miles from it, go figure.
At my end of the BRP, the roads to and from the parkway are mostly narrow/windy roads. The parkway itself is gentle, although you will be climbing and descending. It basically starts at Smoky Mountain NP (the start is within a mile or two of the entrance to Smoky Mountain NP). There are plenty of historical spots along the way.
First stop is the town I live in, Waynesville, NC. Nice historic downtown, worth an afternoon. If you grab a campsite at Pisgah Mountain CG, on the parkway, you can drive the TV to Waynesville, and then back again.
Then the parkway goes through Asheville, NC, so make sure to stop at the Biltmore Estate, and the Grove Park Inn. IF you like beer, Asheville is probably the beer capitol of the SE.
Further north on the parkway you will reach the entrance to Mount Mitchell State Park. I'm kind of surprised the NP service hasn't grabbed it. Highest point in the US east of the Rockies. Continue on north and you will find Grandfather Mountain, another SP, then Linville Falls, Linn Cove Viaduct.
Boone, NC is a nice side trip, college town in the mountains. To the east of this area you have Mt Airy, NC, the town that Mayberry was based on. Stop at Floyd's barber shop, and get a pork chop sandwich at the Snappy Lunch.
As you continue north on the parkway, the elevations drop. Still very nice. All kinds of information on the BRP and Skyline Drive on the web.
Before you get to NC, you should consider Taladega Scenic Highway in Alabama. It basically ends at Cheaha SP, highest point in Alabama and a good place to camp. There is also a road north of there, that is like a min-parkway too, takes you by Little River Canyon, Desoto SP, Desoto Parkway, all the way to Mentone, AL. All very scenic.
Then you might as well continue up to Lookout Mountain and see Chickamauga and Chattanooga National Military Parks. By going this direction, you avoid Atlanta, always a plus particularly when you are towing a trailer!!
Fancy Gap campground is interesting near Mt Airy, as it is a private campground, yet it is essentially on the Blue Ridge Parkway. Fancy Gap is just above the NC/VA border.
I could go on and on, but you get the idea.
In the heat of the summer and into the fall
, people head to the mountains of the SE (yes, we do have mountains).