The Airborne and Special Operations Museum is located in Fayetteville, North Carolina. The Airborne and Special Operations Museum is located in Fayetteville, North Carolina. The main exhibit gallery moves the visitor through time, starting in 1940 with the conception of the U.S. Army Parachute Test Platoon and ending with today's airborne and special operations units. The dramatic 59,000 square-foot building contains a 5,000 square-foot, five-story high open lobby area with two full-sized, fully deployed parachutes..