There are a number of great neighborhoods in and around downtown Indianapolis, that are convenient to IUPUI. I would recommend talking with an agent familiar with the area. There are a few of us who are very well versed.
I just talked to my brother in laws GF, she said the apt she lived in was an all girls apt it was called St. Agnes. It is gated, and I have been there a few times. The inside is really nice...so if you are looking for an all girls apt...you may want to check that one out too.
We really cannot categorize neighborhoods as safe or 'drive by' type neighborhoods. But we can tell you that there is tons of info online for crime reports, and that type of info. The best piece of advice I would say is to take a drive through some areas you are interested in, watch for the surrounding areas and if you start noticing suspicious things just move on. You can always call the local police dept too for that kind of info. Sorry to have to beat around the bush...it's too bad people have to even ask a question like this, and other people tie our hands so we cant say anything:) best of luck!