What time are you arriving? - The best introduction to Manhattan is from the New Jersey shore at dusk, as the lights come on. There are quite a few boat clubs with open bars where you can get a beer and just watch Manhattan come alive.
Pete's Tavern is well worth a visit, - seems funny to go to NY to see a bar based on an English pub but it is a great place.
http://newyork.citysearch.com/profile/7087411/ You need to walk all of the villages, Chinatown, Little Italy etc. Perhaps see the Flat Iron building, - you also need to go downtown on a working day, see the financial district, (wall street is small) best time Friday night 5pm as the bars fill with NY's shrugging off the working week. It's loud. The "it" places vary week on week, you need to hook up with somebody living on the island to know where the action is, - often around new bars opening. NY's always seem to want to be the latest place.
Use the tubes to get a feel for the NY atmosphere, - don't rule out all shops, - Paragon by Union Square is an enormous sports shop.
Museum's - MOMA and The Metropolitan are great, not everybody’s cup of tea.
Ellis Island is good, gives the whole place a sense of perspective. Statue of Liberty, you need to see it but it's a big statue, - it is the view back of Manhattan that is amazing.
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