From direct experience, I would also recommend you avoid the Skyline Drive, which is kinda the northern extension of the Blue Ridge Parkway. This is very heavily patrolled and has a very low speed limit and is more frequented by tourists. Avoid if possible is my advice. To get on the northern end of the BRP, you get on at Waynesboro, VA. A good run would be (weekdays)......:
Day 1: Get to Waynesboro lunchtime-ish.
Waynesboro to Roanoke (the BRP passes very close by).
If you have all day, then get off at the Peaks of Otter and vist the D-Day Memorial at Bedford VA.
Day 2: Roanoke to Tapoco Lodge
This is a longish run, will take most of the day.
Thats the BRP done :-)
Tapoco Lodge is at one end of Deals Gap and not far from the NC end of the Cherohala. www.tapocolodge.com
Day 3: Two loops back to Tapoco Lodge again....
129W thru Deals Gap west to
Foothills Parkway north to
321/441E over Great Smokies (go to the summit at Clingmans Dome) to
Cherokee and thru to Dillsboro to
23 to Franklin
Take 28N (one of the best roads in the area, great to do at a fair clip)
129 to Robbinsville, then
143/165 which is the Cherohala to Tellico Plains.
Back the way you just came (you'll understand why when you get there) to the 129 then N to Tapoco Lodge.
Thats a nice day with 4 classic roads....Deals Gap, Foothills Parkway, 28, Cherohala Skyway....about 280 miles....you'll have had fun on that.