Wrap up warm. Been twice in February. First time there was 25in of snow in one night, and the second time it was miles warmer (but still max temp of 0 degrees!)
Go to Gallaghers for a steak.
Expect to be paying $7-$8 a pint.
If you want to go up some tall buildings to see the views, One World Trade centre is ace for a view of Manhattan from the south of the island, and to see all around NY and NJ. Empire State Building is a great to go up at night, and Rockafeller during the day (you can see Central Park from the Rockafeller centre but not ESB. But if you go up at night you wont be able to see the park).
If you want to go to a show on Broadway, you can get discounted tickets from a booth in Times Sq on the day of the show, but you might be limited as to what is available. Good if you don't have a show in mind you want to see, but if there is something specific then it might be best to book in advance.
But the best advice I could give you would be to just explore for yourself. Its a wonderful city. You can be given loads of recommendations and try to fit things in and then miss out on other things. You'll find loads of things to do, see, places to eat, and drink. And you'll have a top time.