Manhattan will be pretty tough but do-able if you reeeaaally want to. I'd wait until you upgraded and have some more coin available before trying that. Going out to eat or to the bar ain't cheap. Grocery stores are a different ballgame too. Just understand that things you probably take for granted like having an in unit washer and dryer or an elevator for a tall building can be difficult to find in certain parts of the city. They will also cost A LOT. You'll have to be pretty disciplined with your budget because state AND city taxes are no joke. I'm not trying to discourage you, those are just a few things that surprised me when I moved there. There's a ton of things to do and you can really take advantage of your non-rev benefits there.

You should look at Hoboken if you want to work out of EWR. You'll be very close to the city but it's a little more affordable and the apartments tend to have more amenities. It's also way less ugly/dirty than Queens and there are a lot more young professional people. You will probably want a car to get to work if you live there and reserved parking spots can be pretty pricey ($200 a month). However a car is not required at all.