Newark's unfortunate crime rates have no effect on the colleges or the respect given to the students who attend the institutions, don't let anyone tell you otherwise.
A lot of colleges are in unpleasant areas, it doesn't change anyone's credibility. New Brunswick has its fair share of crime in the area as well. As a matter of fact there was just a student from Kean University beaten to death a few blocks away from Rutgers New Brunswick.
The Newark campus is in University Heights, right next door to NJIT which is reputable as well. Seton Hall Law school is also in Newark.
Rutgers has an amazing nursing school that is constantly voted one of the top in the state and best in the country. Newark doesn't take away from that.
Perhaps you really aren't familiar with the area, but this question is borderline offensive for those of us who actually live in the Newark area. Why would any hospital care about the location of a nursing school? Especially a top rated one?
Good luck and congrats on that scholarship!