I recently moved from Manhattan to outside New York (for reasons mostly unrelated to the pandemic; my roommate decided to move in with his significant other, and I didn't want to pay for a 1 BR in Manhattan). The building we used to live in did officially originally say the rent would be increased for the next year, but when we told them we weren't staying, they pivoted and offered us three extra months for free if we signed on. I'm not sure if this is evidence for or against your statement that rent isn't falling much in New York, but I thought it was an interesting data point.
