A New York Hello is when you get introduced to the city in an unfortunate way, or just when something untoward happens in general. Instead of saying "Well that's a fine how do you do" (Laurel and Hardy style) you would say, "Well that's a fine New York Hello".
Having a plant from a fire escape fall and bop you on the head,
or by having a taxi drive by and splash water all over you,
or by having someone spit on you.
That's a fine New York Hello