The GSMNP is a rather large area. You really need to narrow it down a bit. These sites should help you to narrow your choices down a bit. One is a commercial site and the other is the offical GSMNP site. It would take you several visits to really "see" it all. Don't for get to take a jacket with you. It gets a bit cool at night, especially when it rains (I think we may have a wet summer this year). W've been sleeping under a light blanket at night and we are only at 3200ft... far lower than most of the park.
(BTW, for the NP campgrounds, we have found that the "max RV size" usually means that that is the biggest RV that will fit on the smallest site in the campground)