Our friends at Wikipedia describe it this way:
Offutt Air Force Base is a U.S. Air Force base south of Omaha, adjacent to Bellevue in Sarpy County, Nebraska. It is the headquarters of the U.S. Strategic Command (USSTRATCOM), the 557th Weather Wing, and the 55th Wing (55 WG) of the Air Combat Command (ACC), the latter serving as the host unit.
Offutt was brought to popular attention during its SAC period when the command was depicted in the 1955 film Strategic Air Command starring Jimmy Stewart, the 1963 film A Gathering of Eagles starring Rock Hudson, and 1964’s Fail-Safe starring Henry Fonda (which not only claimed to show portions of the base but also a nearby Omaha neighborhood) and Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb starring Peter Sellers (which depicts a nuclear first strike from a mad general at the fictional Burpelson Air Force Base).