Do a bunch of local New York things: Hang out in Central Park, Explore Brooklyn, wear black, enjoy the free WiFi in Bryant Park (use the bathroom there — nice). Attend a lecture at the 92nd ST Y, go to Chinatown in Queens. Buy junk at a street fair, and eat street meat (don’t ask). Have a cigar at the Grand Havana Room (members only). Catch an author speak at a Barnes & Noble (use the bathroom while you are there).
Eventually I hope to write up my How To Be A Pedestrian In NYC guide, a companion to my rules for the NYC subway, only a bit more helpful and less ranty.