I live in Denver and my husband is faculty at Anschutz. With regards to housing:
1. Anschutz is in North Aurora, which is not a good place. I would not recommend living anywhere adjacent to campus, and absolutely don't consider going North of I-70 into the Montbello area. That said, we live in Stapleton, which is a 5-10 minute drive away. It is very family oriented, but does have a fair amount of apartment/condo options. If I had to make an educated guess about costs, I would say rental costs are in the $1500-$1700 range for 1 bedroom and $2000 ish for 2 bedroom.
2. But, if I were single and without kids, I would live closer to downtown (probably on the East side of downtown like Capital Hill, Congress Park, Cheesman Park, Hale etc. If you really want to be close to the action, go into downtown and look at LoDo (lower downtown), RiNo (River North), Speer, the Highlands. Rent is significantly higher in these areas and the commute could be an issue.
3. South/SE Aurora is OK and offers options. If you have kids and can get a school in the Cherry Creek district, that is the way to go.
The rental market in Denver is extremely tight. The city is very desirable and seemingly everyone wants to move here. You have to act early on places.
Here is a map to the neighborhoods in the City and County of Denver. Note, it is city only and does not include Aurora at all. Anschutz (not pictured) can be found to the SE of Stapleton bordering Colfax Avenue.
http://www.denvergov.org/denvermaps/documents/citywide/Neighborhoods.pdf