Awesome to hear you might be coming over to the east coast!
Renting an apartment in NJ (depending on where you'll be living) should be around $1000 a month, give or take a few hundred. And that's just for rent, not necessarily including water/heat/electricity. And on top of that you got cable tv/internet and phone bills, which will add another $1000 or so. As for food, learn how to cook and shop at the grocery store, you'll save tons.
Living in Boston isn't the cheapest area, I pay $1215 for a [larger] room in a 2 bed apartment (with living room) I share with my friend, as well as a parking space. Heat and water is included, we just have to pay for the gas stove and electricity.
Going out to the bars and restaurants throughout the month definitely add up and you can easily spend $100 in just one night out.
As mentioned before, it really depends on where you are in NJ. The NYC area is expensive, but you can find great deals in Brooklyn.
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