These are the areas I'm looking at...
Circled areas are:
Blue: Cheeseman Park and neighboring areas (The area west of Cheesman park seems a little nicer... and further from Colfax is better)
Red: Baker Neighborhood
Purple: Washington Park
I know that there are condos for sale in the Cheeseman Park area for < $200,000 no idea what they're like, though.
Not sure about any of the other areas. All seem to be great places to be either car-free or car-light. Lots of stuff to do, nearby stores, etc.
Cherry Creek Bike Path runs along Cherry Creek... parallel to Speer Blvd for the most part... makes for very easy bike access to downtown.
One of the light rail lines runs down I-25 (Well... two, actually... they split up just south of the Broadway station at I-25 and Broadway)