It's not completely pointless to post this here, as a very high percentage of us are city cyclists, and have dealt with this before. When I got doored, I called up Stuart Leon, who is a bicycle specific attorney based here in Philly. I'm sure there's a similar firm or attorney in NYC. It helps to have someone that works specifically with cycling, as they know the specific laws and loopholes. How about this guy?

In my case I got repairs to my bike paid for, and some extra for minor injuries. Don't talk to the other party's insurance claims adjuster before talking to a lawyer, or at least don't agree to go on record.