Well I am a Vandy undergrad (senior), and I have to say I love both the school and city. People have this stereotype that it's nothing but a hick town, but it's definitely not true. However, I came from a Midwestern city of about the same size (~1 mil), and not from a northeastern megalopolis like you. Nashville has been a GREAT place to live as an undergrad. People here are very friendly and live up to the "Southern hospitality" stereotype. There's not much in the way of public transit, but traffic isn't a huge concern either.
The downtown area and nightlife might be a bit smaller than you are used to, but there are plenty of bars, restaurants, and live music joints. If you absolutely can't stand the thought of being anywhere near country music or ever hearing snatches of songs on the streets, I'd stay away, but otherwise you're sure to find something that suits you. It is Music City USA after all, not Country Music City. There are your more standard clubs about half a mile from campus, which seem fine to me, but might be less glamorous than you are used to. There's museums, parks (a full-size Parthenon replica is just across the street from campus), and other cultural icons, but again, they might not be able to compete to yours.
For sports there is Titans football and Predators hockey, then a minor league baseball team which might be more fitting on a student budget. Vandy itself is in the ultracompetitive SEC conference, but being as small as were are, we often get crushed by public powerhouses like U of Tennessee, Ole Miss, etc. Instead of tailgating, students get dressed up for football games, but the visiting fans--who are often swamp the home fans in numbers--have some pretty huge and elaborate set-ups. We do pretty well in the less televised sports, alright in basketball, but not so hot in football.
Nashville itself is pretty safe, especially for being a fairly large city (~1 million people). There's your occasional theft, but serious crime isn't much of an issue. The "Vanderbubble" as the surrounding area is known is especially safe and well patrolled. Unfortunately though, it can also be somewhat expensive for meager student budgets to live on, but is nothing close to what you'd pay on the coasts. The edge of campus opposite to the med center has occassional problems with bums/panhandlers annoying students for money, but it's not much of a problem. I've never felt threatened anywhere and I'm not exactly the most intimidating figure.
The school itself is top-ranked (ok, not ivy league) but cut-throat is the last word I would ever use to describe it. Everyone seems laid-back, content, and cooperative. I even hear the med students are amongst the happiest anywhere by some survey. The whole student body does have a southern, preppy bent, but oddly enough it is very national in scope. Politically, the students might lean conservative, but this is an ever so slight a tilt. I think it just seems ultra-conservative because our top-20 peers are so liberal. The administration, however, is very progressive, and the Dem students are definitely the more vocal of the two parties.
Hope that helps, but if you have any other questions, feel free to send them along!