MOMA in NYC is closed...they have a branch open in Queens. They will be open at their newly renovated city location Spring '05.
I am assuming your student has never been to NYC. Definately the Met...especially if your student has never been...if you can get tickets to the Blue Man Group and haven't seen them before, that would definately be a cool thing to do. Natural History Museum especially the Planeterium (pardon my spelling), The Hard Rock Cafe, Chinatown, a broadway play. I am mostly thinking of the things I do with people who have never been to NYC before.
Go to websites for the museums and see if there are special programs, etc. If you go to the Empire State Building, go late in the evening, around 9 or 9:30ish....there is no line and the city looks so beautiful at night.
I don't know when you are coming, but if it is in August, be aware the the Republican National Convention is in town and all around Madison Square Garden streets will be blocked off. I would travel by subway some and by taxi some, just to get the flavor of the city.
I am sure others on the list will have much better ideas...hope this helps some! So much to see and do....