Copy/paste from the last time someone asked about NY....
First off - get the
City Pass. If 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 well as getting in free/discounted to hundreds of places).
Additionally - check the arrivals hall and your hotel lobby for discount card racks. You can pick up discounts for all the main attractions from these if you're not doing the City Pass. I know the Macy's visitor centre definitely has them if you don't see them anywhere else.
As for attractions - the "must sees" are:
Empire State Building
Rockerfeller Centre (personally, I prefer this to the ESB)
Central Park (the Zoo is also well worth a visit - although I have heard the Bronx Zoo is supposed to be better)
USS Intrepid (retired aircraft carrier, brilliantly set up with loads of planes on the flight deck)
Statue of Liberty (There's a great immigration exhibition on the island, but if you're not bothered about that, 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. Start at the 34th street end - that way you can walk through Greenwich and all the way down to Chinatown (if you have the legs for it!)
Madison Square Gardens -for NBA/NHL games. 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 Museum - can be crazy busy, but worth it. If you do everything, it's a good part of a day to see the lot.
Guggenhem (didn't like this so much, but the building is amazing)
Museum of Modern Art (MOMA)
Police Museum - brilliant 9/11 exhibition.
Chinatown - South of Canal Street. Knockoff watches/perfume/bags and authentic NY Chinese food(!)
Brooklyn Bridge - amazing bridge, fantastic views of the city - walk across and you can tick off Brooklyn from your visit. Grimaldi's Pizzeria is just under the bridge on the Brooklyn side.
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.
If you want to go to the theatre while you're there - you can get very cheap tickets from the TKTS booths. I'd avoid the Times Square booth as the queues are insane. Go to the South Street Seaport booth instead - get there for opening time and there's not much of a queue. Bear in mind that not all shows are discounted, but there's so much choice, you'll find something you want to see.
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 Metrocard. It's unlimited use and is the best way to get around. IIRC you can get daily, 3 day or weekly passes. Don't bother with buses - they're slow, smelly and rarely go where you want. Taxis are pretty reasonable for short hops - they now all take cards as well as cash.
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. Bear in mind that taxis charge a flat rate from NYC <--> JFK of $52, it's about $60 to and from Newark. Both will drop you at your hotel.
Whatever you do - don't hire a car unless you are planning on spending time away from the city. It costs a bomb and there's no parking anywhere in the city!
Hotels:
I've stayed in a few different places, at different budgets.
The Jazz hostel I stayed in has sadly shut down, but there are others. They're not luxurious, but if you just want somewhere to put your head down, they're a cheap stay.
http://www.jazzhostels.com/jazzonthepark.php
Going upmarket a bit, I loved the Roger Williams Hotel. Lovely rooms, right in the middle of everything. Really nice hotel - but can be pricey.
http://www.therogernewyork.com/#index
Also stayed in the Ace Hotel. Really cool rooms, the bar downstairs is constantly busy and they have an amazing coffee shop in the front. The attached restaurant is award winning as well It's just around the corner from the Empire State (as is the Roger) so you don't have to take a subway to get into town.
https://www.acehotel.com/newyork
Last couple of times, I've stayed in the Pod hotels. Been in both locations, loved the roof terrace on 51, but 39 is just that little bit handier for everything. Both of them have excellent bars nearby. The rooms and beds are pretty compact, but have all the usual amenities - you shouldn't be spending a lot of time in your hotel room anyway!
http://www.thepodhotel.com/
P.S.
Tipping - it takes a while to get used to, but anywhere a service is provided (taxi, concierge, hotel porter, barman, waiter, etc) it is expected to provide a tip.
Here's a quick guide. Bear in mind that many service staff are not paid a minimum wage and do rely on tips to make a living. It's a weird setup, but it is considered very bad form not to tip.