There's lots to do in NYC and you don't necessarily need a ton of cash either. Just going downtown to Greenwich Village and hanging out in Washington Square Park or uptown in Central Park, you could just sit on a bench, eat a sandwich and people watch and take in the sights.
For starters, there are tons of restaurants to choose from. Get the Zagat's Guide to look for restaurant reviews if you're really picky.
There are the usual landmarks that everyone visits (Tony mentioned them): Empire State Building, Statue of Liberty, The Intrepid.
If you're a shop-a-holic like me, head straight to midtown on West 34th Street and "do" the whole block from 5th Avenue (& 34th Street) to 8th Avenue. You'll find Macy's, Sephora, Express, Lane Bryant, Banana Republic, Victoria's Secret, Forever 21, Baker's Shoe Store, The Gap, Payless, Strawberry, Nine West, H&M Clothing, Steve Madden and more! 34th St is the shopping headquarters. There is a subway system and buses you can also catch on 34th street to bring you near to whereever it is that you'll be staying.
In Greenwich Village, on West 8th Street, there are a bunch of shoe stores, plus lots of people watching down there and you can grab a slice of the famous "John's Pizzaria" on Bleecker Street and then walk a block down to grab a cappucino at two really good bakeries on Bleecker Street.
If you're not tired and feel like walking (if not you can either take a taxi or the subway - subway's cheaper) to Little Italy / Chinatown and there you have tons of restaurants to choose from also.
Back uptown on West 46th Street (also known as Restaurant Row) you have tons of restaurants that people usually go to after they see a show on Broadway.
For shopping at designer and pricier shops you could venture up and down Madison Avenue or 57th Street from East to West. (more expensive shops there).
When the time comes, if you need more detailed information, just send me a message. I was born and raised in NYC - so I'm familiar with it.