I concur with terryallen. Once you hit I-40 just head west. Plenty of campgrounds to choose from seeing you only want overnight stops. Timing may be essential when going thru the bigger cities like Nashville and Memphis, they can be nightmares traffic wise. Asheville is fine usually, Knoxville is fine outside of rush hour time. The Pigeon River Gorge is not that scary turn and grade wise but its mostly down hill so gear down and don't ride your brakes. Oklahoma City can be quite busy but after Oklahoma City its pretty much clear sailing. Safe travels to you.
