Why not NYC? i feel like people say NYC is expensive but do not calculate the savings you get from no car and that you can live outside of Manhattan. Newark is cheaper than NYC but that comes at a cost, you probably would want a car so car cost, there are less things to do in newark and most of newark is quiet after like 7pm. Idk if you are single or not but more social/romantic activities if you are into than in NYC.

Also it is much easier to find roommates in nyc if you are down for that.

NJ taxes are pretty comparable to nyc taxes so you do not save there and much more job opportunities in NYC.

Really research and see if you can live in nyc. Look at brooklyn, downtown manhattan, and queens basically anywhere with good subway access. Since you are not looking to move in the high demand months (summer) it should be cheaper.

TL;DR: look at nyc, the cost might not be as bad as it seems

Good luck, make that move!