We just drove in November (from Niagara Falls). Seems to me they were on the north end of 77 right near Virginia/West Virginia border. There are two tunnels, they are both long-ish (nearly 1 mile long I think). Can't remember exactly but one is a bit shorter than the other. The BIG downhill (Appalachian) mountain is at the north of North Carolina on 77.
The longest stretch for me feels like West Virginia.
Good luck on your trip!