I should probably note for those who see this thread in the future that I'm nearly a year out of the program, so my knowledge about specific academic policies, classes, etc for the MENP is rapidly going out-of-date.
As for living - I still do suggest Edgewater and Rogers Park. They're both on the Red Line, which means that you have easy access to the Lincoln Park campus and many of the hospitals DePaul uses for clinicals. Other than the far NE corner of Rogers Park, the area is as safe as anyplace else on the North Side, and is much quieter at night as it serves as a "bedroom community" for those who work elsewhere in the city and the near-north burbs. Speaking of which, Evanston might be another possible place for you to look for an apartment - the suburb is served by the Purple line, which goes express between Howard and Belmont during the morning and evening rush, which is also convenient for DePaul students.
I found my school apartment, as well as my new one, through Craigslist. However, if you're going that route to find a place to live, you really need to crash on someone's couch in the city or otherwise be in- or near-town so that you can follow-up inquiries with apartment viewings until you find a place. If your apartment-hunting visit is on a tight schedule, I'd suggest using an apartment-hunting agency, of which there are a few. They're free to use, as the landlords pay them to find new renters.
Congrats on getting in!