If you order through Life Extension, they'll mail you a blood draw kit if you are able to arrange your own blood draw. I've been told that if you contact their customer service, they will point you to local service to have it drawn. I think you'll have to pay for the draw services.
If you're near the border of another state, it could be worth doing a price comparison with the providers mentioned on my individual test pages, since many of them only care about the state in which the blood is drawn.
That's all I'm aware of for New York. If I've missed anything, please let me know in the comments so I can list more options for residents.