You could try NYC's CityLore: http://www.citylore.org/

Also, there is the Center for Traditional Music and Dance in NY: http://www.ctmd.org/

NY Pinewoods is the folk music society there:   http://www.folkmusicny.org/

There are many field recordings at the Library of Congress' Archive of Folk Culture that were made in NYC, including some of Alan Lomax's recordings of ex-NYC sailors. Full listing here: http://www.loc.gov/folklife/guides/NewYork.html

Another great resource is back issues of the New York Folklore Quarterly (1945-1974). Tables of contents for all back issues can be browsed here: http://www.nyfolklore.org/pubs/nyfq/tocnyfq.html

I have recently been on a search for similar material from Long Island, so PM me if you are interested in that as well.