Green's Dictionary of Slang is a highly regarded and well-curated dictionary that I would feel safe calling "the best online slang dictionary" in a holistic sense. Because the The website is easy to use, and with a paid subscriptionwith a paid subscription you can access its massive collection of citations, I find it usefulnow available for starting answers on this site that involve slang, whether recent or historical, by seeing what citations exist so far.
(I have no affiliation with GDoS, I just like itfree without a subscription.)
But evenEven with GDoS, the granularity is not to the level of "New York." You could search for words or senses formed in the U.S. between 1910 and 1919, and optionally specify cultural context in searching, but if you really want to find slang unique to New York in 1910, you might consider seeking out texts that were published around that point in spacetime, or sociological works specific to that culture.