In Nashville the Hermitage is a must see. What are you looking for in a park? Resort style with high end amenities? A basic site with W/E/S? Have you gone to the TN state parks website to see what the parks have to offer. TN has great state parks and they can be difficult to get into at high demand times. Your interests and time frame would be helpful to give you better ideas.
There are 2 private parks on Music Valley Drive and all of them are FHU and nice. We have stayed at Yogi Bears Jellystone park a few times and its clean and more than acceptable. 2 Rivers is right next to it and it is nice too. A Camping World is right up the road too.