score:7
Can I fly to New York from abroad, stay 4 days, and then leave abroad?
Yes (obviously assuming you're allowed to enter the US and the subsequent destination country, which you may verify via IATA).
https://coronavirus.health.ny.gov/system/files/documents/2020/07/nys-covid-travel-advisory-faq_0.pdf (mirror):
Travelers from designated states may leave the state prior to the expiration of the 14-day quarantine period. However, to protect the public wherever you are, you should still maintain quarantine for the remainder of the 14-day period. Travelers are responsible for their own expenses during quarantine.
FYI same question for California: Am I allowed to go to the airport to catch a flight if I am supposed to self-quarantine in California, United States?