I am so glad to see that you are happily pregnant!
I know how you feel about having to go a hospital that is in a bad area. My mom had to go to Columbia Presbyterian Hospital. It is in a very bad area of the Bronx. While the hospital grounds were completely safe if you strayed one block too far you were in a war zone. I remember praying that we didn't have car trouble driving through to the hospital. I am a person who grew up in a city environment and I would visit Manhattan often too but this really was a whole different ball game.
Anyhow back to you, when I was pregnant we were going to use St. Peter's Children's hospital. It is an excellent hospital although unfortunately it is base in New Brunswick as well although I was looking at their site and it says that they have a transport team. I do know hospitals transfer infants to that hospital all the time. It is one (if not the best) best hospitals for NICU care in the state. Also, Robert Wood Johnson (which is not too far away is also an excellent hospital).
Here is their link I don't know if I helped you or not since you are saying New Brunswick is too far. I'm from north central Jersey so I don't know too many hospitals in your area.
Here is their link
http://www.childrenshospitalspuh.com/>