Only thing I can really say is North Omaha is the only bad part of Omaha I'm aware of, having lived in the Omaha/Lincoln area my whole life. West Omaha is good, but you'd live farther away (about 30 minute drive away). Creighton is in pretty much downtown Omaha, the area around there isn't that bad actually, though it's older. I've had friends live on about 50th and Dodge growing up, and Creighton is roughly 24th and Dodge. And the University of Nebraska-Omaha is at 60th and Dodge, so that whole area isn't a really dangerous place.
Compared to larger cities, Omaha doesn't really have many bad areas. You could likely just use Creightons gym, which I have no idea how good or bad it is but since you'll be a student it'd be free im pretty sure.
Wish I could give more, but really I don't think there are many places outside North Omaha that anyone I know would purposely avoid.