In "Kansas City" you'll find a small style point and a larger exercise in balancing common sense with copy-editor geekiness. (Also, I understand, some crazy little women.)
Most stylebooks leave "Kansas City" off their "dateline cities" lists, meaning that you must specify in datelines and on first reference "Kansas City, Mo." or "Kansas City, Kan." Your common-sense instincts might say, "Aw, c'mon, of course 'Kansas City' alone means the big city in Missouri and not the not-so-big city in Kansas!"
But listen to your geek side on this one. For every 10 people who know that Kansas City means Kansas City, Mo., there are probably three who "know" that you're leaving off the Kansas part because it's part of the city's name. If you mean the Missouri city alone, you need to spell that out.
On the other hand, don't let the stylebook bully you into insisting on a state in references to the Kansas City area or Kansas City television and radio stations or even Kansas City-style barbecue.