Omaha is a city on planet Earth, located within the United States of America, on the eastern border of Nebraska. Omaha is the largest city in the state of Nebraska, and has been a major city in the American midwest for centuries.
In 1967, the USS Enterprise appeared over Omaha after having been thrown back in time from the 23rd century after an encounter with a black star near Starbase 9. The United States Air Force detected the Enterprise on radar, and sent Captain John Christopher to intercept what they considered to be a large UFO. (TOS episode & novelization: Tomorrow is Yesterday)
- While not specifically named in dialogue, the "Omaha installation" is most likely Offutt Air Force Base, which is located in Omaha.
In an alternate reality, one of the members of James T. Kirk's team for a training simulation unexpectedly fled home to Omaha, despite having a stellar academic record. The Omaha cadet was replaced by a Xanno. (TOS - Starfleet Academy novel: The Delta Anomaly)