I've thought about it and the way I've figured, the de facto capital building where the legislature of the government was to take place should be in a major city that is not serving as the capital of a nation, state/province, and should be a culturally, economically, and perhaps even spiritually diverse area. To my knowledge, the only city upon that list that qualifies would be New York since all of the other cities listed already serve as the capitals of their respective nations. Also, the UN is headquartered in New York City and it saves the time of constructing a new building.
However, I put "de facto" capital because it would be unwise and rather insane to have the entire government of a planet located in one area. Other international organizations would be converted to serve the needs of a planetary nation and would be headquartered in other major cities across the globe to better serve the needs of the global administration.