I think that the majority of the soldiers live in the Fountain/Widefield area. Those towns have affordable housing and are close by. However, as you fear, the crime rate in those places is not good.
I suggest you look at the Skyway neighborhood (essentially top of 8th Street over to 21st Street). There are some affordable places in the area, it has a decent crime rate, and it is in one of the top school districts in the state. The most popular biking destinations in town -- like Jones Park, Captain Jack, The Chutes, Stratton Open Space, Section 16, Red Rock Park -- are all within an easy pedal distance of a couple miles.
Another place you may consider, if you want a sleepy, old-fashioned lifestyle, is Florence. It is at the edge of your commute time (probably more like 20-25 minutes), but it is an easy drive south of the post on highway 115. There aren't a lot of trails in the immediate vicinity, but the Wet Mountains and the Sangres are close to the south, and Canyon City is starting to get some reasonable trails built around town. Those are great outdoor recreation areas.