The short answer is he's being a selfish asshole.
The bigger answer is you need to both sit down calmly to discuss what you're going to do. You clearly need some extra help with your daughter, and he, as the father, should provide that. Where in NJ do you live? Where does he go to school? There are some parts of NJ that may as well be in NYC. Besides, what the hell is he doing in NYC that he can't do in NJ? I'm in grad school as well, and while I enjoy parts of living in Chicago, I know I'm not 100% utilizing the city because I'm busy. If I had a child and SO on top of that, I don't think it'd matter if I lived in a city or a remote part of the country. I simply wouldn't have enough time to do well in school and be a respectable parent and SO.
Being in NJ doesn't have to become permanent, and if it does, that's his own fault. Living in NYC (I assume you're referring to the city and not part of the state) is really expensive. You'd both save money living together period and living in NJ is much cheaper.
Depending on where in NJ you live, perhaps you could live farther from your mother but closer to the city.