We have traveled from north Alabama to Utah/Colorado the last 2 summers and always need to stop for the night in Arkansas along I-40. I have not found anything between Little Rock and Memphis. There is a KOA jut off I-40 in Little Rock but some of their sites are good and some are horrible. There seems to be more camping around Fort Smith, and one or two places we have stayed between Fort Smith and Little Rock.
Never been from Memphis to Nashville, but I would bet there is more camping available on that leg than the LR/Memphis leg.