Start off by seeing the city's sights. Things to see are not lacking in this town, so you should choose just a couple of highlights or even one neighborhood a day to explore. Coupling the Statue of Liberty with Battery Park and either Ellis Island or the National Museum of the American Indian will be easy as they are all within a short distance of each other.
Slalom through the packed streets of Chinatown. You can couple this with a visit to Little Italy, which is engulfed by Chinatown. Head to Central Park afterward if you're going to the Metropolitan Museum. Wandering through brash Times Square should be a part of your trip to see a Broadway stage show.
Eat your way through New York. When you begin to tire from sightseeing you will need to eat. Just about every group from every part of the globe has a community in New York. For you, this means it's not difficult to find authentic cuisine. If you're craving Dominican Food, take the train to Washington Heights. For Russian Food, go to Brighton Beach. For Turkish cuisine head to Sunnyside, Queens.
Check out some of the local favorites as well. In the East Village there is Xunta, a Spanish Tapas Bar that makes often ordered pitchers of Sangria. If you're interested in soul food, make your way to Sylvia's in Harlem. For arguably the best barbecue in the city, go to Virgil's in Times Square.
Choose how you want to spend your evenings. After cleaning up for a night on the town you will need to decide which type of entertainment suits you. Easier said than done as New York is an entertainment hub. Midtown means the lullaby of Broadway, as well as a few large venues for touring acts and sports franchises. Classical music is conducted uptown at Lincoln Center and Carnegie Hall.
Seek out the up and coming performers as well. New York is one of the great testing grounds for those trying to break in to the entertainment industry. You can often see world-class performances in spaces not much larger than your living room. Off-Off Broadway theaters, rock clubs, small galleries, converted dance spaces and many others flourish in the city and are worth your time.