Anise, if I weren’t so agoraphobia, we would be hanging out in all the same places!
AnnaLucretia, you will not have trouble finding funky Nashville things to do on Broadway which is the main drag that cuts through downtown. Restaurant, bars, live music. (Music Row is mostly recording studios and is further away.)
There are also plenty of places to explore on the side streets.
The most famous dive bar is Tootsie Orchid Lounge on Broadway (also referred to as Broad). Every country singer and fan has cried into a beer there.
The best general source of information about Nashville is probably this one:
http://www.nashscene.com/
About a week ahead of time, you should be able to check the Arts column on the left for live music to see what is happening where. They also have dining recommendations. I hear the Patrick’s downtown on Broad is good and the Stockyard too.
Someone mentioned the Parthenon. Most of the exterior is an exact repelica of the original in Athens. It would be an easy taxi or bus ride out West End. I think Springwater is alongside the park where the Parthenon is. If I remember correctly, it is a for real dive and not just a tourist dive.
Other places downtown: The Frist Art Museum, Ryman Auditorium (the original home of the Grand Ole Opry), the Country Music Hall of Fame, the Tennessee Performing Arts Center, 2nd Avenue, Riverfront Park for a cruise on the riverboat and live music.
People watching can be great on Broadway. Just remember that the weirdest ones are tourists. 
You can always play it by ear. Plenty of places to check out. Do inquire about the special discount coupons on tours of the sequin mines.
You will not need dress up clothes in Nashville unless you want to wear them. Anything goes.