That comes out to about $2000 a month after taxes. That's pretty reasonable. The academic housing wouldn't be a bad option as long as all utilities are included and it's within walking distance of the academic buildings which would save you on a metrocard. That would also ensure a certain standard of living and probably be much less of a hassle for you. Quite frankly, finding an apartment here is difficult even if you're a long term resident, but you're at an even larger disadvantage if you're an international student. The requirements are stringent to the point of ridiculousness(e.g. income of 40x the rent, bank statements showing source of income & savings, high American credit score). Every single international student I know has been made to pay 3-12 months of rent in advance, which is not only a major financial burden, but also a terrible idea as it puts you at risk if you have a bad landlord or roommate.
New York, otherwise, is not that expensive if you're careful and you take certain precautions(buy your weekly or monthly metrocard with a debit card just in case you lose it!). Most things are actually fairly affordable and there's always something to do. Happy to help if you have any other questions.
