My ex-wife earned her Bachelor's and Master's degrees at Vandy while we were dating/engaged. From my experience, I would say Vanderbilt is fairly safe, and that the students are more in danger of being victimized by a classmate than someone from outside the school.
While Vandy is right downtown, it is in a fairly affluent area. There are less affluent areas not too far away, but the Vandy and Metro PD's and Vandy security do a pretty good job of patrolling campus and the area around it. I remember hearing about suspicious persons being reported on campus, as well as some violent crimes (robberies and the occasional rape/attempted rape). But, those are fairly infrequent and the school has taken steps to safeguard the student body. For example, the campus is pretty well lit, there are police/security call boxes all over campus, and students can call security for escorts across campus, if they feel the need.
Additionally, from what I saw, the Vandy campus is pretty tight, meaning the students tend to hang out socially with each other. They are frequently, it seems, going places in groups, which lessens the likelihood anybody is going to try to take advantage of them. Also, many of the students live either on campus or very close to it. They're less likely to live in places such as Antioch or Bordeaux-two of the less reputable neighborhoods in the city.
The downside to them spending so much time together is the fact that they can often become too comfortable with each other, often resulting in them lowering their guard, which can result in victimization from those closest to them. Whether it's a roommate stealing from them, a drunken fight at a party, or a case of date rape, there is always the potential for people who spend lots of time together to become predator/prey. One example would be the
case of the football player who encouraged his teammates to rape a drunken female.
In short, Vandy, like any other school, has some safety issues; but, they aren't nearly as bad as many other schools. MTSU, in nearby Murfreesboro, for example, has a little bit more of a problem with crime than Vandy does. And I say that as an MTSU alum. Of course, it's much easier for the criminal element from the lower income areas of Memphis, Nashville, and other cities to be accepted to, and afford, MTSU.