Spendy but lovely restaurant: Scarpetta 355 W 14th St.
Grimaldi's in Brooklyn Heights (yes, you will see a ton of dubs, but trust me, it is worth the sacrifice). Great pizza--get there early and prepare to stand in line.
Ninja New York is a fabulous food experience. Even if you just go for drinks, it is worth a trip to their bathrooms (featured on the Travel Channel).
Shopping: Century 21 and of course Saks Fifth Avenue. If you are a make up junkie like I am, hit up Sephora.
Wicked is an awesome musical to see while you are there.
I am envious of your plans--hope you have a blast!