Also - try to catch a Yankees Game. The new stadium is great and only a subway ride from Grand Central.
I would also rent a bike a and ride the pth along the West Side Highway.
I take my jetski down the hudson every weekend and always envision the black and white pictures of all the steam ships up and down the hudson in the harbor and imagine myself as part of that. Crazy me huh?
I would also check out Broadway just to walk around and get the feel of the hustle and bustle of the city.
and dont eat at the tourist traps! you will get ripped off!
Go to Little Italy and its not that expensive at all.
I will be going to the Mets/Twins...may try to squeeze in a Yankee stadium tour if time permits.
Just as important as where to go...where should I avoid?