The buildings, all heavily decorated with neo-Gothic and Tudoresque motifs, are arranged in a U-shape that opens to the west. The eastern facades of the towers have significantly fewer windows than their western counterparts.
These two design decisions were made primarily to protect the residents from the stenches coming from the waterfront. Only later, as the United Nations was developed and the views of Queens becoming more interesting, did it seem like a bad decision to provide so few windows.
The interiors of the apartments are configured to face west, and considering the landmarked status of the building, adding easterly windows seems unlikely. In fact, because it's a landmark, the large neon “Tudor City” sign that for years has been turned off at the request of the UN—they believed it interfered with their communication equipment—has not been removed, despite its rust and precarious position, for fear of altering the appearance of the building.