A clue can perhaps be found in these alternate versions of a video she made, perhaps shortly after the audio session, in which she druggily lip-syncs to it while photographed, Warhol-style, in a single, unflnching shot. One version is of the video itself, while in the other it is projected during some sort of performance at the Squat Theater.
video version: https://www.youtube.com/watch?v=rLHDifZhPpc
Squat version: https://www.youtube.com/watch?v=EyaVt0dcrjY

It does seem clear that the Squat Theater was integral to the impetus for Nico to do this song. Located on W. 23rd St. a few doors down from the Chelsea Hotel, the Squat was the domain of a group of refugee activist/actors from Hungary, led by the parents of Eszter Balint of Stranger Than Paradise fame. While never a member of the company per se, for a number of years Nico "squatted" at the theater's space, and was the closest thing she had to a regular address in New York.
The video performance of "New York New York" appears to have been made with this one public display of it in mind, and for all I know the audio session was made for the same purpose. Any info on Nico's "New York" episode would be greatly appreciated.
--Phil