Here's a list of roads you can try while you're in the Southern Appalachia (in and bordering North Carolina). I give you my word, just spending the day on any subset below, would be worth the trip from anywhere within a two-day drive. Just let me know when you get done with these, and I'll post more. I'm going "road finding" NW of Asheville, NC next weekend.
NC 80 - Marion, NC to Loafers Glory, NC (The Devil's Whip and beyond)
NC 226A - Marion, NC to Little Switzerland, NC
NC 197 - Erwin, TN to Pensacola, NC (and on to the end of the pavement
Double Island Road - Micaville, NC to NC 197
Hanging Rock Road - Spruce Pine, NC
Crabtree Road - Little Switzerland, NC to Micaville, NC
Bear Wallow Road/Seven Mile Ridge - Little Switzerland, NC to South Toe
19E - Spruce Pine, NC to Elk Park, TN
19W - Micaville to Erwin, TN-ish.
NC 126/South Mountains Institute/Lake James Road - Morganton, NC to Marion, NC
NC 181 - Morganton, NC to Pineola, NC
NC 90/Brown Mountain Beach Road - Lenoir, NC to Steele Creek
NC 268 - Lenoir, NC to Wilkesboro, NC
Champion Road/Lewis Fork Road - Ferguson, NC to US 421
Parsonville Road/Summit Road/Falls Road - Wilkesboro, NC to Boone, NC
Boomer Road/Russell Gap Road - Boomer, NC to Taylorsville, NC
Sulphur Springs Road/Brushy Mountain Road - Hiddenite, NC to Wilkesboro, NC
Oklahoma Road - Roaring Gap, NC
Haystack Road - Roaring Gap, NC
Lambsburg Road - Lambsburg, NC to Blue Ridge Parkway
Bear Trail - Cana, VA
Orchard Gap Road - Cana, VA to Blue Ridge Parkway
Squirrel Spur Road - Ararat, VA to Blue Ridge Parkway
Bat Cave Road - Old Fort, NC to Bat Cave, NC
NC 9 - Bat Cave, NC to Black Mountain, NC
NC 74 - Bat Cave, NC to Asheville, NC
NC 151 - BRP to Asheville, NC (or just to the bottom and back)
NC 276 - Brevard, NC to Waynesville, NC
NC 215 - Brevard, NC to Canton, NC
NC 28 - Highlands, NC to Fontana Village, NC (and on to the end)
Ellijay Road - Franklin, NC to Cullowhee, NC
Buck Creek Road - Highlands, NC to Franklin, NC
Wayah Road - Topton, NC to Franklin, NC
US 129 - Robbinsville, NC to Chilhowee Lake, TN
Wolf Pen Gap Road - GA 60 to US 19, Blairsville, GA
US 19 - Blairsville, GA to Dahlonega, GA
GA 60 - US 19 to Morganton, GA
Richard B Russell Scenic Byway - Helen, GA to Blairsville, GA
US 221 - Linville, NC to Blowing Rock, NC
Shulls Mill Road - Blowing Rock, NC to Boone, NC
NC 194 - Valle Crucis, NC to Banner Elk, NC
Georges Gap Road - Sugar Grove to Bethel
3 Top Road - Creston, NC to Todd, NC
Meat Camp Road - Boone, NC to Creston, NC
TN 67/NC 88 - Trade TN to West Jefferson, NC
Old Hwy 16 - West Jefferson, NC to Grassy Creek, VA
NC 194 - Jefferson, NC to Boone, NC
US 421 - Mountain City, TN to South Holston Lake
US 58 - Damascus, VA to Mouth of Wilson, VA
VA 16 - Mouth of Wilson, VA to Tazewell, VA
Comers Rock Road - (I don't know a town, but it comes off of Hwy 21, North of Independence, VA)
Old Bridle Creek Drive/Turkey Knob Road (VA 601) - Independence, VA to Sparta, NC
Scenic Highway/Stoney Fork Road (US 52) - Wytheville, VA to Bland, VA
Grapefield Road - Tazewell, VA - Bastian, VA
Burkes Garden Road - Tazewell, VA to Burkes Garden, VA
I should clarify - The locations on the roads are mostly towns I know. Some roads start or end outside those towns, sometimes as much as 15-20 miles. If you have trouble locating anything, let me know. I included very small towns near my home, because I know their names. Some examples of "near misses":
226A starts about 10 miles North of Marion, off US 221.
197 is 395 at the Erwin, TN end.
Both ends of Parsonville Road/Summit/Falls Road are between Boone and Wilkesboro.
NC 215 starts 5 or 10 miles south of Brevard.
So, just take a quick look at the map or Google Maps, and you'll find them in the general area.