I worked for a few years as an EMT an a couple as a medic in NYC up until 10/07. I did a couple of months at Hunter Ambulance, and did the rest of my time at NSLIJ CEMS. I also worked for the Flushing/Jamaica/Brookdale system.
Many area hospitals want some 911 experience, usually 6 months or more before considering you for hire. If you have the connect, then you might be able to get on without any 911. You could apply to FDNY EMS, and either go to medic school on their dime, or use them as 911 experience and get into a good, high paying hospital. NSLIJ gives medic scholarships to their personnel.
The NREMt-P is needed by many out of state employers in order to receive reciprocity - this is when another state recognizes your cert and issues you one from their state. Some medic programs will include it. I had to go out and do it on my own. I needed it both for Charleston County EMS and Fairfax County Fire Rescue.
If you do the NY Methodist paramedic program, try to get Tony Thomas if you can.
I enjoyed my time in NY, but the quality of life sucks, I'm making more than I was before I left, and my dollar goes way farther. I was born and raised in Ridgewood Queens (Cypress/DeKalb, Seneca/Gates, Gorver Cleveland HS). Not the worst area, but I knew that there was much better out there.