Not all. NY hasn't yet expanded eligibility to international residents, unlike some states like PA (other than Philadelphia) and TX which are okay vaccinating anyone of the right age regardless of country of residence.
Source:
https://covid19vaccine.health.ny.gov/ "All individuals 12 years of age and older that reside in the United States are eligible to receive the vaccine."
https://www1.nyc.gov/site/doh/covid/covid-19-vaccine-eligibi... used to mention this requirement but still links to the NY State COVID-19 Vaccine Form (seemingly hosted on S3!) https://forms.ny.gov/s3/vaccine that includes an attestation that the vaccine recipient "presently reside[s] in the United States".
They aren't just excluding international tourists, either - lots of non-tourist international residents are still excluded from vaccination in NY. I'm an American citizen who currently lives outside the US, but I've spent most of my life living in NYC and am preparing to move back there with my wife once she gets her US immigrant visa. We recently visited my fully vaccinated parents, primarily as a family visit and
mental health break, and with tourism kept to a minimum for safety reasons.
When we got our first shots in late April, the rules were "NY residents only", so we each got our two doses in a relatively nearby, rural, and somewhat politically purplish part of PA that had plenty of spare shots and that didn't mind ID documents showing foreign residency. Even now we wouldn't qualify for getting our first dose in NYC, despite having a lot stronger ties to the area than tourists.
I hope NY removes this last restriction some time soon: maybe together with its so-called "full reopening" on July 1, maybe when the Canada-US land border reopens to travelers who aren't fully vaccinated, or maybe when the geographical travel restrictions get dropped for foreigners coming from the EU/UK/China.