Depends on what you like to do. NYC is a pretty huge place. I'm going to assume you like Japanese stuff at least a little so if you're downtown in the East Village, you can check out:
http://nymag.com/listings/stores/toy-tokyo/
It's an interesting little store, and right next to it is a place specializing in fries, they have like 30+ sauces to choose from (I like the garlic mayo). You can take the 6 train to Astor place, have lunch at:
http://newyork.citysearch.com/profile/7087442/?brand=smx_restaurant-nc
on Broadway (get a burger for sure, they are quite big), and take a walk down St. Mark's Place (exit the diner and head straight towards the big black cube) to 2nd Ave, where you turn right to get to the toy shop. It's still an interesting block with some funky stores, even though it is much tamed and yuppified from the old days (you can buy comics, bongs, food from an automat, weird expensive Zen meditation stuff, get a tattoo/piercing, etc, yeah it's a long block).
There's also a ton of shopping you can do along Broadway (turn right after exiting Cozy Soup and Burger). There are plenty of train stops along Broadway when you get tired. If you want good prices on brand name stuff though, I'd suggest Century 21, it's right next to Ground Zero, where they still haven't really built anything yet. From there, you can also visit City Hall.
Of course there's also the usual touristy stuff, Statue of Liberty, Chinatown, South Street Seaport to see the "waterfalls" they installed under the Brooklyn Bridge, Empire State Building, Times Square, museums (I'd recommend the Metropolitan Museum of Art, it's humongous though, it's also "suggested admission", so you can pay anything, but I just like to pay the student price, if they ask you for student ID just say you left it at home. I like the detailed carvings on the old guns in the weapons section), Central Park. I would definitely suggest buying or printing out a map to carry around with you.