Yup, West 4th Street get labeled WEST but most stations don't get East or West labels. but there is a reason--(likewise, my subway stop is 63rd Drive Rego Park.)
Logwood wanted to know how to treat the word east in an address- and no one in manhattan lives at ### 23(rd) Street.
they live a ### EAST 23(rd) Street or ### WEST 23(rd) Street. that is how its written on the envelop for a mailing address, and that what we say. "i live on EAST (or WEST) number street. (we might not immediately share our house number, but we will often say which street.)
reguarding the subway, i think the reason there that some stations are called EAST or WEST is because each station needs to have a specific name, unique name. so all 3 42nd Street stops have names.(Grand Central,5th Avenue, and Times Square--not only for the #7 train, but for the uptown/downtown trains-- 2,3,6, the D, F, and 1,4, E, A, C. -- even back when they were the IRT, IND and BMT, the individual companies would want to be able to tell stations apart.
On the east side, the local #6 station is 33rd Street, but on the west side, the IRT stops at 34th. (and the D,F,R,N all stop on 32nd street.
all of those station extend from 32nd street to 34th Street-(and have 2 or more exits) so if you says 33rd street station, you can only mean the east side local. (on the west side, one of the 34th street stations is 34th street/Penn Station (the IRT) the other is just 34th street(the IND) --once again creating unique names.
There is a 4th street station on the east side. (which is called Astor place instead of East 4th Street) Unique name requirements are why West 4th Street station is WEST.
(and you know there are 2 main exits. West 3rd street or West 8th Street-- there is no exit to West 4th street.)
