WTC memorial site you won't see much of because they have a giant ass wall around it due to ongoing construction. You have to get a ticket to visit the actual memorial (they're free...goto their website and reserve a time), at which point you can go inside. It's easy enough to see the new buildings being constructed, though.
Empire State Building is basically just an office building...I assume you just want to go to the top and look? It gives you a good view of the city, but be prepared to wait a long ass time (and you gotta buy a ticket).
For museums, the Metropolitan Art Museum (not just famous art like stuff from Van Gogh, but also ancient artifacts from Egypt/Rome/etc) and the Natural History Museums are musts, IMO. They are world class museums with amazing collections.