Okay, besides the bars which, if you're a first time visitor to Nashville you MUST SEE...
If you're into architecture, and even if you're not be sure to go see the Parthenon--at night especially but you might want to see it in the daytime too. Just take my word on this.
If you like gothic revival architecture there is an interesting church over near Vanderbilt. Scarritt Bennett's Wightman Chapel looks like something straight out of England--like a little St. Paul's Cathedral or Canterbury or something. Also there is a church designed by William Strickland with Egyptian Revival architecture (Downtown Presbyterian). It is considered a masterpiece. Doesn't look like much on the outside...inside is another story.
And of course you'll want to see the Ryman Auditorium, which is right off Broadway and the Naked People statue at the Music Square Roundabout. I forget its real name, everyone calls it that. If you like Art Deco, stop in and see the Frist Museum. Used to be the main post office and it was renovated in the original style. It's right next to Union Station, now a hotel but it has maintained a lot of its original charm from when it was a train station. While you're there, head into the Flying Saucer Draught Emporium and start earning yourself a plate on the wall.