Kansas City was the name of two neighboring cities on Earth's North American continent. One city was in the state of Kansas, and the other was in the state of Missouri. Often the area was collectively referred to as "Kansas City". The area was noted for its great contributions to the musical form of jazz and the distinct type of steak named for it.
In 2364, while looking for a suitable location for a recreated holographic jazz club, Commander William T. Riker first suggested Kansas City before changing the locale to New Orleans. (TNG: "11001001")
When the crew of the USS Enterprise-D encountered a group of cryogenically-frozen Humans from the 20th century near the Romulan Neutral Zone later that year, one of the survivors, L.Q. Clemonds, ordered a Kansas City strip steak as a meal before deciding on a martini instead. (TNG: "The Neutral Zone")
While participating in a holodeck program set in the Ancient West, Worf asked the barmaid Annie Meyers for some "Klingon firewine," only to be told, "This ain't Kansas City! We ain't got none of that fancy European stuff here!" (TNG: "A Fistful of Datas")