The blue ridge parkway is available if you drive north to Ashville. It will take you up into Virginia. The speed limit is 45mph or less so it is not the quick way. It is a very scenic route with lots of stopping for pictures opportunities. At near 45 mph it is not a challenging drive at all. There are turns but they are gradual. If you google "blue ridge parkway" you can get a free map with recommendations of places to stop along the way. If you have more time, you could go south in North Carolina a bit to the "tail of the dragon". It's a much more fun drive but quite short. There are scenic and fun to drive roads you can take on the way there. And you can pick up the south end of the BRP close to the tail of the dragon. Googling "tail of the dragon" will get you more information including a free map of the scenic roads in North Carolina.
If it fits your schedule, I stayed at the Osceola Mill B&B and really enjoyed it. It is an old converted mill with about 6 nice rooms and a restaurant on the first floor. It's less than 5 miles off the BRP and the road that takes you there starts out as a bit of a drivers road. It's hard to get to the speed limit and stay on the road, in other words.