I think that East and West are definately part of the street name(in NYC)--and since don't East and West appear on street signs? Look again (peter the Rock for a head!) the font is usually smaller, but its there!
some streets (West4th, or West 96th, are better known, and used to define a neighborhood, but 400 West 20th (chelsea city housing projects) if very different from 400 East 20th ST., Grammercy Park (a lovely neighborhood centered around NYC only private park)
(in law & order, they often have address that don't exist--like 600 East 42nd street--(which if it existed would be somewhere in the middle of the east river!)
NYC also has and East End Avenue(only a few blocks long) and West End Avenue.
5th Avenue ends at 8th street, a the north end of the Greenwich Square park, At the south end of the park, the east/west division line moves one block west, to broadway.
