Start with the university housing office. He might be eligible for an apartment (not the same as a dorm room for undergraduates) in a building for graduate students; these are often operated on a coop or nonprofit basis. The housing office should have rental listings in locations that are convenient to campus as well as information about leases, buildings or landlords to avoid, etc.

The university is likely to also have an office that provides services to vets; it might have access to additional housing resources or know of landlords who favor vets.

Otherwise, check city and local/suburban newspapers (and city weekly papers or city monthly magazines) for ads, google or use websites like apartments.com, the apartment website that pops up periodically on FT as a sponsored thread (ad), grocery store and university (perhaps in the student union) bulletin boards, drive around neighborhoods of interest to spot "for rent" signs, read the past business section of the newspaper and any city business newspaper to find articles about or notices of new buildings that are opening now,

Are his expectations regarding price, size, amenities, newness, location, etc. realistic?