There are three campsites located in Victor Road. Victor Road is approx. 2 miles north of highway 80 (highway 80 is is approx 16 miles north of Mount Mitchell) on the Blue Ridge Parkway. The road is initially pavement but quickly turns to packed gravel. The road is a little rough in spots, but I had zero issues in my Honda Accord. Sites are free and do not appear to be managed by any official municipal, state or federal authority...but they are in great shape.
Three sites are available from what I could see. The marker on this map is at the site of what I am calling #3. Sites 1 & 2 are located about 1/2 mile down Victor Road on the left and are adjacent to one another, but appear to be large and have foliage separating them. One of the sites had three tents pitched along side a beach tent and still had plenty of open space in the middle around a stone fire pit. I stayed at site number three. This has enough room for two cars and a four person tent at most. I have a three person tent and it covered most of the flat pad area. The site has a fire pit and is located just before a large(ish) stream that crosses the road. Beyond this campsite, the road turns private. The site is on the left hand side as you approach the stream. There is room on the right hands side of the road for perhaps another tent if one wanted to do so.
This is fairly remote, despite being close enough to the BRP to hear cars occasionally. There are no amenities aside from the fire pit, but it's handy to have a creek for water for filtering or boiling. You should note that there are hunting blinds at the top of the hill between sites 1/2 and 3. These are facing a field that points away from the campsites. I imagine during turkey season (I saw a lot of turkey), you may hear gunshots.
There aren't any trails down this road, but you are within a few minutes of the BRP where they are plentiful and Mt. Mitchell and associated trail systems are less than 20 minutes. The BRP would have to be open for you to access these sites, so plan accordingly (my suggestion is the real time map on nps.org).