Don't miss the Parthenon, the Rhimaen (spelling issue but the original Grand Old Opera). For food my favorite is Prince's Hot Chicken Shack ( literally order your food through a hole in the wall).
Not sure when you are planning to visit, but you should check out the Christmas decoration at Opryland Hotel. You will want to hit Music Row and check out the live music and restaurants. You can visit a variety of historical sites just south of Nashville in Franklin. There is also the Jack Daniels Distillery that has tours available. If you have time, try to eat at Loveless Cafe. Depending on the shows available, you may want to get tickets to the Opry now. Oh and you could do a cruise on the General Jackson Riverboat. I'll try to add some more later.
I know it should go without saying, but since you're going to the music capital of the world, you should check out where it all began... Sun Records! (note, link contains audio)
Crap! Hught is correct, sort of (and didn't need to delete her post) (historic) 706 Union Ave. Memphis, Tennessee 38103 (current) 3106 Belmont Blvd. Nashville, Tennessee 37212
Nashville I was there just a few weeks ago on business. In our spare time, we visited Opryland Hotel, the Hermitage, and the downtown district for music and food!! I was amazed at the quality and reasonable prices at the restaurants downtown, although they do get you on the parking fees. Big River Grille, Jack's BBQ, and Demo's were all recommendations from local folks, and they were all excellent!!
Although not as cool as the plant tour in Memphis, Gibson gives tours of their Nashville facility (near Opryland). Due to legal issues in the last few months you might check before showing up.