New York to start vaccinating people with certain health conditions on February 15.
Starting February 15, New York will enter the second phase of its COVID vaccine distribution and allow people with specified health conditions to get the vaccine. The first phase focused essentially on health care workers, teachers, and people over the age of 65; the next phase focuses on people with the following conditions:
Cancer (current or in remission, including 9/11-related cancers)
Chronic kidney disease
Pulmonary Disease, including but not limited to, COPD (chronic obstructive pulmonary disease), asthma (moderate-to-severe), pulmonary fibrosis, cystic fibrosis, and 9/11 related pulmonary diseases
Intellectual and Developmental Disabilities including Down Syndrome
Heart conditions, including but not limited to heart failure, coronary artery disease, cardiomyopathies, or hypertension (high blood pressure)
Immunocompromised state (weakened immune system) including but not limited to solid organ transplant or from blood or bone marrow transplant, immune deficiencies, HIV, use of corticosteroids, use of other immune weakening medicines, or other causes
Severe Obesity (BMI 40 kg/m2), Obesity (body mass index [BMI] of 30 kg/m2 or higher but < 40 kg/m2)
Pregnancy
Sickle cell disease or Thalassemia
Type 1 or 2 diabetes mellitus
Cerebrovascular disease (affects blood vessels and blood supply to the brain)
Neurologic conditions including but not limited to Alzheimer's Disease or dementia
Liver disease
Source: https://covid19vaccine.health.ny.gov/phased-distribution-vaccine. You can see if you’re eligible to get the vaccine by taking this screener: https://am-i-eligible.covid19vaccine.health.ny.gov/Public/prescreener. Note that you must show one of the following to prove eligibility: doctor's letter, medical information evidencing the condition, or a “signed certification” that you have the condition (though it is not totally clear to me what the state will accept for this last category).
Nearby locations for an appointment are the Javits Center and the Walgreens on 30th Street between 10th and 11th Avenues: https://vaccinefinder.nyc.gov/locations.