Using the Good Sam trip planner, from NYC to Nashville is 883 miles. Wow, you plan on one overnight stop? That's some long days driving, then again I'm old and retired so I have the luxury to take my time. 
Do the Good Sam trip planner and see what CG's might suit your needs. Plenty of options. As far as Nashville goes we have stayed at Yogi Bears Jellystone  just off the Briley Parkway on Music Valley Drive. Then right next door is 2 rivers CG, both are nice campgrounds and the closest to downtown. Camping World is just up the road too.