NYC will be way worse if you have to sleep, or eat, or spange. Food is ridiculously expensive, everyone will steal your shit if you're sleeping on a bench, and everyone that lives there is asked for change about 5,000 times a day so they won't even acknowledge your existence.
I don't know about all of northern NJ, but generally, I wouldn't recommend being in NJ or NYC at all. Hitchhiking is illegal in NJ, and all the trains that roll through are low-volume and super sparse... it's really hard to get out.
That being said, if you really want to go to NYC, send me a message with your phone number (if you have a phone) and I might be able to put you in touch with someone who will let you crash at their place for a night or two. No promises though.