From The Stargate Omnipedia
High-security U.S. government facility, built in the early 1960's and housed within a mountain near the city of Colorado Springs, Colorado.
Cheyenne Mountain is the location of NORAD and Stargate Command. Level 3 is Accounting. Sublevel 28 includes the Gate room, control center, and conference room.
BEHIND THE SCENES
This fictional home of Stargate Command is actually a real location in Colorado Springs, Colorado. Inside is a room with a door labeled "Stargate Command." The room is a broom closet.
Though Cheyenne Mountain is currently closed, Stargate Command remains in the base in the fictional universe. For now.
Children of the Gods - After an invasion from Apophis, Cheyenne Mountain becomes the front line for Stargate Command's base of operations.
A Matter of Time - The Stargate connects to a world being destroyed by a black hole and, in the process, the mountain complex suffers severe time distortions. Hammond orders the mountain evacuated.
Foothold - Stargate Command is overrun by an alien species bent on replacing the base personnel with themselves.
Chain Reaction - The mountain is nearly destroyed by radiation pouring through the Stargate after a failed experiment on another world by the S.G.C.'s new commander.
Zero Hour - Parts of the complex become a gardener's nightmare after an alien plant gets out of control.