I would go south on US-19 to Elizabethton TN. Then take US-321 south toward Boone NC. Take NC 105 bypass to NC105 back to US-321.
It's going to be up, down and around. I have driven the Elizabethton TN to Boone NC part pulling our 5'th wheel. 35-40 most all the way, but the curves arn't so sharp that I couldn't stay in my own lane. Of course you can take I-81 south to I-26 south to I-40 east. But that adds a lot of miles