I know of an excellent cat specialist in Clarksville, TN which is about 45 minutes from Nashville. If you can't find a good vet in Nashville, let me know and I'll PM the info about the one in Clarksville.
I just recently moved to NJ. This is what we did to find a new vet.
First we checked the yellow pages. Made phone calls. Then went down to the actual offices and looked around. Are they clean/are they willing to spend time w/me to answer my questions. Check w/neighbors to see who they use.
Actually, we had to take my Streak to the [serious here] feline dermatologist for an [skin] allergy. It wound up being quite a ride for us and her office was part of a animal trauma center -with a staff of feline specialists. We asked her to recommend, or help us write out some questions to ask. She was extremely helpful. Then we check the yel pages, etc.
And the trauma center doesn't lose us as a customer because after an emergency w/our other cat....we were able to have constant care for our Nuki and able to vist any time during their office hours which are 24/7!!