I am originally from Blowing Rock, NC which is fairly close to Banner Elk, it may be a bit of drive from Banner Elk but not quite sure. If you go down in an area called globe there is gravel for days. Was there for the weekend of the 4th and just rode my mtb but a proper gravel bike would be fine. First day I took road bike down into globe and double flatted so I decided to just bring too much bike.

https://racesonline.com/...obe-gravel-challenge

the whole area of globe has great gravel last day did a section of road called maple sally which was about 37mi and around 4500ft of gain.

EDIT: Was looking at a map if you can connect from Banner Elk to a "Town" called Gragg that is where all the gravel is and I am sure that route would be gravel and see if you can connect to a road call Watauga river road that's towards Valle crucis.