The Academy has a great 3d Range and there are opportunites to hunt on base with a bow. I'm retired Air Force and never got stationed there but went TDY a few times. Also the Eastern Plains has some great mule deer & whitetail hunting but a lot is private.
I have done a lot of exploring around the Springs. One of my best friends was in the Air Force stationed at the Springs. We rode most all the trails around on dirt bikes. My friend started a mapping business while stationed there so we rode and rated the trails. We climbed Mt Baldy and were working toward racing up Pikes Peak. My friend left the Springs for Great Falls where we raced snowmobiles in West Yellowstone before the enviros closed the town in winter.
I think you will enjoy the area, there is much to do, depends on what you like to do.
I forgot to thank you for your service. Thanks for your service!