Can't speak for Vandy but Nashville is a great city. It's a southern city so it's a little more on the conservative side, but besides that it's great. Lots of things to do and places to see. Lots of really cool people to meet, and the crime isn't as bad as most cities of the same size (bar a few neighborhoods here and there).
Like I said, it's a southern city so if you've lived in the northeast you're entire life it might take a little while to get used to, but otherwise, great place.
Not to sound dickish but if your a girl, your hot, and you join a sorority, then you will have a good social life handed to you. Vandy social life/parties are centered around greek life and if your not apart of greek life than it will be a little more difficult for you but it also depends on your general personality. If you're an outgoing and fun person you will attract people like you and you'll have fun, if you're shy and don't talk to anybody you'll stay lonely. Pretty basic stuff.
Downtown nashville/broadway is pretty fun and there's a lot of stuff you can do on the weekends (clubs, restaurants, karaoke, laser tag, etc.)
Most of the "mainstream" social scene revolves around Greek life. Fraternities drink and play pong typically every tuesday/thursday. Girls and rushes are always there. Tend to be like 6 or so major fraternity parties every weekend that people party-hop between.
Vandy tends to be know as the only elite school that actually has a good party scene, but maybe I'm biased.
There is certainly a social life to be had outside of Greek life, as the majority of the school (60%?) is independent, but I don't know much about it. Lots of fun bars and such in downtown Nashville.
Aside from frat parties on campus, which my daughter doesn't tell me about it detail, I know that she went to several concerts/shows in N'ville this past year ranging from small venues to the Tennessee Performing Arts Center and the Bridgestone Arena. She doesn't have a car to get downtown but there is easy access to cabs that will take the Commodore card as payment. Likewise, the lack of a car did not hinder her ability to go to the movie theater or go shopping at Green Hills mall (fairly high end) that you can get to by bus which also takes the Commodore card. She went to a country karaoke bar and Shakespeare in Centennial Park...as another poster said the possibilities are endless.
Vanderbilt is loved by Nashville. This is actually one of the plus factors in attending there just as Chapel Hill is loved by North Carolina and Virginians love UVA.
Secondly, Nashville is a seat of state government and a major player in business in its region. There are many many internship options and Nashville is a whole lot more fun than say....Hanover, New Hampshire. Or many other host towns of great colleges and universities. It isn't Chicago. Or New York. Or Atlanta or Boston. But it is a fine host city. Lots of artists and lots of scientists. And a decent economy.
You're a freshman girl. You (or at least all of the girls on your hall) go to frat parties, and the parties the frats throw on Demunbreun St Thursday nights. Frats love freshman girls, and you love them. You think this is the height of life. No wait, Lonnie's karaoke after fratting is the height of life.
You're a sophmore. You're a frat pro, and an awesome dancer after so much practice last year. You still dress up for frat theme parties, but you don't try too hard like the freshman girls. Pregames at Vandy-Barnard and Towers parties spice life up. Lonnie's is still classic, but not better than chik-fil-a branscomb breakfast at 2 am.
You're a junior, and suddenly questioning if you're too old for frat parties after a can of beer gets sprayed over the crowd you're in. You're tired of freshmen asking you to dance. When you turn 21, you don't look twice at frat row, save the occasional off-campus frat gathering. You hit Flying Saucer on Mondays, Sportsman's (or Whiskey Kitchen if you're super classy) on Tuesdays, Patterson House if you have $ to blow, cheap concerts at 12th and Porter and Club Mai, The Stage, Paradise Park, and Demunbreun St on weekends.... but the only reason you're really going out is to drag people to Lonnie's afterward.
Senior Year, you have bigger concerns than partying, like internships, med school interviews, honors theses, and job applications. So maybe you only go out twice a week now. You check off different "bucket-list" bars and parties, and you pretend you're a freshman all over again once or twice, but really, you just want to go where you know you like. Lonnie's.
This has been my personal experience (or, how I have partied over the years,) and seems pretty standard. There are lots of people who don't engage in any of this and go to entirely different parties than I did, or don't go to parties because they stay in with their boyfriend most nights or because they have real work to get done or because they're off camping/hiking/rafting every weekend with the outdoor club. Some people only go to Belmont Univ parties. Some people rage in McGill dorm every night. And EVERYONE has a niche, so don't worry if you don't think what I described above is for you because you'll fit in just fine.
^ My friend at Vandy said pretty much the same thing. Frat parties are fun for a while, he says, but the day you turn 21, head out to town. There's so many great restaurants, bars, and pubs in the area that you won't even look back at frat life for a second.