Be aware that they may try and apply resort tax, we refused t pay it, look it up.
Well we have bee not New York several times and always had a great time. We checked out load of famous sites inc;
The Empire State Building (it's immaculate worth a visit - bought tickets from a street guy who gave us a free entry to Top of the Rock which we visited at night, that was pretty good)
Hudson Yards - Nice shopping centre and worth visiting even it just to admire The Vessel
Katz's is the famous delicatessen, with fabulous sandwiches also where the filmed the very famous 'where Harry Met Sally Scene' - See Here
Times Square with you will struggle to avoid but after a few days will do your best to avoid lol (I would suggest eating away from Times Square as it is expensive!)
Washington Square Park is a lovely area and one of our favourite places to visit. (also place were many movies used) See the red house on the right of the Arch, that's where
Robert Neville (Will Smith) lived in the film - see here - Ghost Busters was also filmed here look it up. But it is a nice place to just go and chill and have a coffee while people watching.
Dumbo (or DUMBO, short for Down Under the Manhattan Bridge Overpass) is a neighbourhood in the New York City borough of Brooklyn. The area known as Dumbo. There are some good eateries and bars and good place to take some photographs by the Hudson River facing Manhattan.
I'll add some more places later.