NORAD and NORTHCOM are NOT in colorado springs or cheyenne mountain. The govt is lying and in this case that is good. They should lie about something like that.
I visited C Springs for a week in 1999, to help out at my company location there. My hotel room had a great view of Cheyenne Mountain.
In 1985 the USAF personnel system screwed up and I was given two assignments, one to Cheyenne Mountain and one to Key West. Sadly, I chose Key West Naval Station.
In my defense, it had just snowed, and a warm place seemed very attractive.