From NYC.gov:

All New Yorkers 16 years of age and older are now eligible to be vaccinated! People who work or study in New York are also eligible. (Note, people who are 16 or 17 years old can only receive the Pfizer vaccine.)

Three COVID-19 vaccines have been authorized for use in the U.S. by the Food and Drug Administration (FDA): Pfizer-BioNTech (Pfizer), Moderna and Johnson & Johnson/Janssen (Johnson & Johnson). These vaccines have been shown to be very safe and effective in protecting people from severe COVID-19 illness, hospitalization and death. As of March 1, tens of millions of doses of vaccine have been administered in the U.S.

These vaccines are the best protection we have against COVID-19. No matter how old you are, COVID-19 can lead to complications and death. Even if you had COVID-19, it is important to get vaccinated because it lowers your risk of getting COVID-19 again and may prevent you from passing it on to others.

Also, getting vaccinated may protect those around you, particularly people who cannot get the vaccine, such as children. Vaccination, along with other prevention measures, can help us end the COVID-19 public health emergency.

Here are some ways to find a vaccination appointment:

TurboVax

NYC COVID-19 Vaccine Finder

NYC COVID-19 Appointment Scheduler

NYC Health & Hospitals

NY State Appointment Scheduler

Additionally, here are some tips about when appointments often become available from different suppliers:

CVS Pharmacy appointments often appear between 12AM and 1AM.

Walgreens/Duan Reade appointments usually appear later in the week.

NYC COVID-19 Appointment Scheduler is updated every 15 minutes, but more appointments appear between 11:45PM and 12AM.

NY State Appointment Scheduler is updated every 5 minutes.

NYC Health & Hospitals also has more appointments at around 12AM.