Quarantine Rule in New York

From the New York State Covid Website:

Asymptomatic travelers entering New York from another country, U.S. state, or territory are no longer required to test or quarantine as of April 10, 2021. Quarantine, consistent with the CDC recommendations, is still recommended for all travelers who are not fully vaccinated or have not recovered from laboratory confirmed COVID-19 during the previous 3 months. Symptomatic travelers must immediately self-isolate and contact the local health department or their healthcare providers to determine if they should seek COVID-19 testing.

So technically you don't have to quarantine, however it also says:

CDC and NYS recommend delaying international travel until the traveler is fully vaccinated.

And from the CDC After International Travel, quarantine is still recommended for international travel for unvaccinated people. (However IMHO there seems to be a grey area between being unvaccinated and having only 1 of a 2 shot vaccination.)

After travel information for people fully vaccinated with an FDA-authorized vaccine or a vaccine authorized for emergency use by the World Health Organization:

• Get tested with a viral test 3-5 days after travel.

  • If your test is positive, isolate yourself to protect others from getting infected.

• Self-monitor for COVID-19 symptoms; isolate and get tested if you develop symptoms.

• Follow all state and local recommendations or requirements after travel.

After travel information for unvaccinated people:

• Get tested with a viral test 3-5 days after travel AND stay home and self-quarantine for a full 7 days after travel.

  • Even if you test negative, stay home and self-quarantine for the full 7 days.

  • If your test is positive, isolate yourself to protect others from getting infected.

• If you don’t get tested, stay home and self-quarantine for 10 days after travel.

So while quarantine is technically not required, it is still the recommended thing to do. In addition, traveling internationally is not recommended, and I'd say even more so if you are only doing this for tourist reasons.

As for tourist attractions, that is an unknown as I have no idea what you consider to be a tourist attraction. For all I know you want to visit NYC to see the National Museum of mathematics (which is currently closed)