Welcome to Arizona. There are homes to rent with two car garages that can be rented for <$1,000 in many areas.
ASU in Tempe and Midwestern Universtiy in Glendale are about 30-40 miles apart from each other. So unless you wish to live closer to one instead of the other or somewhere equally in between, there will many places to choose from. Are you going to off campus locations for Midwestern or actually to the Glendale Campus? Being close to things, other than the commute, may be a prudent factor to consider.
Rather than choosing a location and a price, let your Realtor know what types of things you like doing (hiking, biking, tennis, golf, shopping, dining, art galleries, sports etc.). This would help the Realtor finding the right place and neighborhood for you. There is no cost to you to use a Realtor that will represent you as the renter or buyer.
In terms of safety, here is a crime hotspot map that allows you to zoom in and see the incidents of crime block by block. Notice the "red zones" have the highest crime reported: http://www.trulia.com/crime/?ecampaign=anews&eurl=www.trulia.com%252Fcrime#
The rents are lower in Glendale than Tempe.
Jeff Masich, Realtor
Arizona Homes and Land, LLC