Being an experienced traveler, I hope you have looked long and hard at the GSMNP web site to determine what areas are open, and what is closed. Several of the campgrounds in the park are closed due to the recent cuts, others due to flood or weather damage. As you have a 5th wheel, the only two sensible campgrounds IN the park to stay are Smokemont on the Cherokee NC side, and Elkmont on the Tennessee side.
GSMNP is unique in its layout as it is not so much a park you enter and then fan out to various places within, but rather you enter various places from the outside of the park. US 441 thru the park from Cherokee to Gatlinburg is the only major road passing thru the park.
I am not familiar with places to stay OUTSIDE the park on either side, except that the private campgrounds on the NC side tend to be small and junky, though there are a few gems also. You will have much better luck on the Tennessee side finding a decent RV campground or resort and will find that much of what you want to see in the park is on the Tennessee side anyhow.
The most natural route from Charleston to the park is to take I-26 to Ashville. Be aware there may still be construction south of Ashville on 26. At Ashville take I-40 west to where US 74 branches off of it at Lake Junaluska, AND FOLLOW US 74 TO CHEROKEE.
DO NOT take US 19 to Cherokee, the section that is on Tribal land (Soco Falls to Cherokee) is narrow, winding and has guard rails right on the edge of the pavement. I pulled a trailer up it once and vowed to never again do that. Be aware that Waynesville in particular, and other areas, received a lot of flood damage from the storm last year.
Stop at the Oconaluftee Visitor Center on the Cherokee side of the park to buy your $2 per day vehicle pass. (America the Beautiful passes and senior passes not valid, you have to pay for the vehicle parking pass)
Both this visitor center and the one on the Tennessee side at Sugarlands are both well worth the time to stop and take a tour of them, lots of displays in them.
RV's are allowed to travel on 441 (aka Newfound Gap Road) thru the park, but commercial traffic is not. Its a good road all the way (unless there is flood damage) and the strangest part is the 360° loop at about mile post 9. It is on the Tennessee side after you have passed over the gap and have begun descending the west side of the ridge. Go slow on 441, you will see bears, and be prepared for bear jams, as traffic stops to gawk at them.
Hopefully others will chime in on private campgrounds suitable for a 5th wheel on the Tennessee side.
As a side note, the Blue Ridge Parkway (BRP) in NC is still closed (and not something you can pull a 5th wheel on anyhow, on the southern end of it, due to the low tunnels.)
While I normally visit this area every summer to get to higher elevations where it is cooler, I will not this summer due to the flood damage.
Charles