Memphis- Tom Sawyers in West memphis Arkansas on the river. I have never stayed tere but others have spoken highly of it.
Nashville- Yogi Bear Jellystne
Two Rivers
The KOA
all are on Music Valley Drive and not too far out of the city center.
Gatlinburg- That depends on if you want in or near G'burg or if Pigeon Forge is acceptble or even Seviervile. There are so many choices here. For G'burg they are all located east of town on 321 and most are acceptable with some nicer than others. Look them up.
Pigeon Forge I can say The Ridge is new and very nice but high priced being a mile north of Dollywood. Pine Mountain is a little way off the parkway and nice.
River Plantation is nice also.