I would say that building equity is always better than renting, at least for that length of time. Housing in the Vanderbilt area continues to have a strong demand, so if you stay for 3 years, you should be able to expect a reasonable return on your investment in a home.
I'm working with someone else who wants to walk to Vanderbilt too. It is a little challenging to find a ton of options for houses that suits ones needs, tastes and budget range within walking distance to Vanderbilt, but they are certainly out there if you have flexibility in your criteria. Houses will most likely be older, so you may not have much of a choice for age unless it was a recent tear down where investors rebuilt it from scratch.
Now if you're open to condos or townhomes, there are tons and tons of options that fit the "new" category within walking distance. Your price range, amenities requirements and unit size requirements will help narrow down the plethora of options for condos.
If you're looking more for convenience and extremely low maintenance, the condo route might be a good option for you. On the other hand, houses are a little harder to come by within walking distance to Vanderbilt, so capitalizing on that might be instead be for you. It all depends on what is most important to you in the place you live, your lifestyle, needs and criteria.
Either way, I say if the prices work for your budget, buy!