Hey, I'll be there too! I live three hours away on Memphis and always visit Nashville in March to visit friends.
Definitely visit the Parthenon, in Centennial Park. Cameras and tripods are permitted to get a shot of the massive statue of Athena Parthenos, but I think there's a no-flash rule. The lighting inside is dim, so bring your cable release. The Hermitage, Andrew Jackson's home, is also in the Nashville area.
My favorite place to eat there is a brewery/restaurant called Blackstone ("nice" but casual) and the Gerst Haus serves authentic German food, with enough variety to suit anybody.