I just visited there a couple weeks ago. There are LOTs of apartment options within walking distance, and house rentals too if you know people. There are even more options within a 10 minute drive, if you want to pay for parking, which will be $30 a month. It's a little bit tight right now because they deconstructed one of the undergrad dorms so there's a throng of undergrads occupying typical grad rentals, but it will hopefully be finished in time for summer lease-signing. Within walking distance studio apts. were $650-700 / mo. and 1-bedrooms around $900 / mo. Vandy's stipends are good (at least for my program, ~$27k), and those grad students don't have much trouble getting by.
Also you get free bus passage with student ID. One prof. suggested getting a first-year 8/9 month lease at a nearby place and riding the bus. When you meet your cohort you can probably find some good roommates.