If you're worried about handing over your life savings in exchange for a set of keys, call the landlord or owner and make sure your agreement is above board. Also, don't get so excited about finding that apartment that you sign on to spending more money on rent than you can actually afford. When you're living on tap water and ramen that next month, you will regret it. New York City's public transportation system will take you everywhere, from Coney Island to the Bronx Zoo and back to the West Village for a night of comedy, jazz, and everything else you might expect out of New York nightlife. There are restaurants everywhere, and you certainly won't have to travel an hour for good Indian food anymore.
Central Park offers a variety of fun things to do outside, from rollerblading to rowboating.
There is also free theatre in Central Park and elsewhere in the summer, and free movies and concerts all over the city, for those willing to wait in line for tickets. The New Yorker , Time Out New York , and the New York Magazine all provide a detailed list of all the things going on in the five boroughs that week.