The first statewide summary of the coming effects of climate change on New York State has been just released by the New York State Energy Research and Development Authority, and things don't bode well for the region. In fact New York is set to experience disproportionate effects compared to other areas nearby.
The NYSERDA reports notes that New York has already experienced warming about twice the global average over the past 40 years, with temperatures rising 2.4°F. An additional 1.5-3°F temperature rise is expected by 2020, with up to 9°F by 2080.
As for sea level rise, due to the effect of currents and other factors, New York has received about 12" of sea level rise over the past century, 5" more than the global average. By 2080, the New York coastline is likely to see 8-23" of sea level rise—up to 55" if melting in Greenland and West Antarctica accelerates.
This level of sea level rise would put the NYC subway system at risk of extreme flooding once a decade, instead of once every hundred years, as is the case now.
As for other effects of climate change coming to New York, on farmlands, tourism, and more, read: Responding to Climate Change in New York State [PDF]