Been a few times, I absolutely love the place!
First off - get the
City Pass. As it's your first time, you'll get a load of use out of it. The bonus is that you save on queue times,as you can usually buy your tickets away from the standard queue.
As for attractions - the "must sees" are:
Empire State Building
Rockerfeller Centre (Radio City is nearby as well)
Central Park (the Zoo is also well worth a visit)
USS Intrepid (retired aircraft carrier, brilliantly set up with loads of planes on the flight deck)
Statue of Liberty (save yourself time and just take the free Staten Island Ferry instead)
Grand Central Station - amazing architecture, loads of shops. Worth a quick spin through.
Times Square - yes, it's tourist central, but it's amazing by day and even more spectacular at night. If you get someone offering you comedy tickets - take them. Been a couple times and they get some very decent comedians in. Ask about drink minimums though
Highline Park - converted railway tracks turned into a park in the air. Not been yet, but it's supposed to be fantastic
Madison Square Gardens - sadly no NBA tickets to be had as they're on lockout, but you should be able to pick up NHL tickets for the Rangers. Check the USA ticketmaster site and select "will call" to pick up your tickets on the night. Also do the tour, it's well worth it.
Natural History Musem
Guggenhem
Museum of Modern Art (MOMA)
I'd also add:
Police Museum - brilliant 9/11 exhibition.
If you have time, Atlantic City is great. I did it as an overnight in the middle of my NY stay. It's got some great outlet stores and the casinos are pretty decent.
Shopping:
Macys - go to the visitor centre on the mezzanine with your passport and you'll get a 10% discount card
Century 21 - TK Maxx on steroids. Amazing range of cut price clothes, shoes etc. It's absolute chaos, but I have stocked up there time and time again. It's also right next to Wall Street and the WTC, so you can chalk them off at the same time.
J&R Electronics/B&H Photo - the two best electronics shops. B&H is brilliant for cameras (duh)
5th Avenue is the place to go for all your brand name shops. Start at the Apple Store on 59th and work your way down.
Transport:
Get a weekly Metrocard. It's unlimited use and is the best way to get around. Don't bother with buses. Taxis are pretty reasonable for short hops.
I'd also recommend taking a taxi or Airbus (shuttle service) into New York - the view as you come in is amazing, especially at night.