You could roll yourself in flour and go as a survivor of the world trade centre - okay that's really sick I apologise, but unfortunately that's what comes to mind when i think of New York.
Films : Breakfast At Tiffany's, On The Town (sailors!!), any Woody Allen movie. Studio 54 (Bianca Jagger on a white horse!), The New York Yankees, Sex And The City, Friends, Will & Grace. To name but a few!
the big apple ....get a big piece of cardboard cut it out like and apple....attach other peice of card in shape of worm coming out of the apple with words "ah fugedaboutit" coming out of the worms mouth..
If you want a really easy costume get a very large cardboard box to wear, print off some piccies of the NY skyline from Google images then stick them on. You could be the whole of Manhattan!