It is not known for certain that "rag time" can be claimed for New York City. However, when the Brooklyn Eagle newspaper went online in 2003 on the Brooklyn Public Library's web site, I found our earliest "rag time" in that publication.
6 September 1896, Brooklyn Daily Eagle, pg. 4:
The novelty of the performance is Ben R. Harvey, who ought to interest students of American music and should have been seen and heard by Dr. Dvorak. He invents and plays what he calls rag time airs and dances, the effect of syncopations being to make the melody ragged. This is real American music; not of the highest order, but genuine.
18 October 1896, Chicago Daily Tribune, pg. 43:
"Darky" music, both instrumental and vocal, is the reigning fad of the hour. Dvorak is indirectly responsible for this, say the music-men, and the negro music of the present time is vastly in advance of what it used to be. The old regular and monotonous "tum tum" of the supposed banjo has been supplanted by syncopated, or, in darky parlance, "rag" time, and the harmonics are much better than of old.