Best of luck to you.
1 bed 1 bath in Park Hill (great neighborhood, great building) - $1,099 (all utilities included)
1 bed 1 bath near University of Denver (I-25 and Evans) - $929 a month
2 bed 2 bath near Lowry with washer and dryer in unit(Alameda and I-25) - $1,049 a month
I'd say your best bet may be over in the Lowry area (Alameda and I-25). It's about 20 minutes away from Downtown Denver, and there are some complexes in that area that have 1 bed 1 bath condos with a washer/ dryer in the unit. If you keep your eye out, you might find one in the $800-$900 range.
If you have any questions about rentals, I have 4 rental properties myself in the Denver area, and know the local rental market well!
How many bedrooms, just 1? Any pets? Any particulars you wish to be close to other than downtown itself?
Craigslist is a great source for listed places by owners ( and can be where scammers are as well), so would start there. I have a know other on-line sources i like, if you want to email me I can send them your way.
Velocity Real Estate & Investments, Inc.