The Al Hirschfeld Free Health Clinic.
It says right on the front: For the uninsured in performing arts and entertainment.
(that includes the underinsured as well.)
The Clinic is a program of The Actors Fund, which I could not say enough good things about. An amazing organization, that helps people get jobs, find homes, find insurance, and also keeps them healthy.
You must make an appointment, 212-489-1939, and meet certain criteria to prove that you're a performer (union card, pay stubs, even playbills). They offer primary care, specialty care and referrals, preventative care (flu shots, mammograms) and counseling. It's located near Lincoln Center.
I haven't gone myself, but I've talked to dozens of actors who have. Also, I once talked to a dancer who broke his foot, and racked up $15,000 of medical bills at the emergency room. He called The Actors Fund out of desperation, and a mediator argued it down to $150. Wow, right?
You're not alone! And though Sarah Palin and Mitt Romney don't care about you having health care... The Actors Fund does.