Hey there. . .when I first came here, I had 2 weeks to find a place. Check out http://www.craigslist.org
. Many ppl post there. You should look in brooklyn and/or New Jersey for less expensive options. Now if money is not object, then the skies the limit, but you probably won't spend much time there so spend wisely.
Areas to consider in Brooklyn: Brooklyn Heights, Park Slope, Clinton Hill, Bed-Stuy (progressively getting better), Bay Ridge.
In Jersey: Hoboken, Jersey City, Union City - trendy areas that are popular for younger ppl.
Good luck. As for the test, you should take the $250 lost, you'll make it back quick in your probably high paying NYC job.
Focus on the move and reschedule once you've settled down. It would end up being a waste anyway if you didn't do well because of all the stress and anxiety right now.