Importantly, the United Nations was not in New York until 1952 (decided at the first General Assembly held at London in 1946).

It seems that the question of location was decided at the Yalta Conference in 1945. Having had a look through some of the Conference Papers, it was officially announced on 11 February 1945 the details of the United Nations Conference - including its location at San Francisco Link to relevant page from FRUS, Conferences at Malta and Yalta, 1945

An earlier plenary meeting on the 8th discussed the issue and decided it should be held in the United States
Link

A memorandum of the same day for matters to discuss with Roosevelt mentions location, although the footnote annoyingly says these are lost! Link

I couldn't find any more specific information than that sorry

Based on a book on the history of the NSA I read a few years ago (so I might not be totally correct in my recollection), the NSA had a big hand in it as they wanted to be able to have an "ear" to the ground and as this was shortly after the war a lot of their techs were on the Westcoast where they had been involved with Japanese cyphers etc.

Please correct me if I am wrong, it's been a decade since I read that book.