Have you been on the TN State Parks web site for making a res. and seeing if there is even an opening when you want to go? FCF is the most popular park in the state I understand and can be hard to get into. The web site has interactive maps in which you can get the info on every site in the campground as to depth, width, level or incline and amp service, even a picture, all you need to know. I have not been there myself so I can't speak as to the road but as others have said you should have no problems. Just check the web site and go from there.
