I'd echo above vis super-zoom compacts / bridge cameras.
As far as New-York trip goes.... most important thing ISN'T in the camera sales blurb.. dont matter how many mega-pixies its got or X-Rated the zoom, or whether it has umpety 'shooting modes'.... it's whether YOU can actually use it..
An awful lot of my 'life-time' holidays happened before digital; (and kidz!) and my constant companion was a very 'humble' 35mm 'Compact' camera, with a fixed 35mm lens, probably less sophisticated than a camera-phone as far as 'point & shoot' snapping goes; BUT, I was very very 'familiar' with the thing. It was small, and 'unobtrusive', or probably more importantly 'un-intrusive'; It was always with me, never 'in the way', and when I saw anything I wanted a photo of; it was in my hand, at my eye, and the snap was shot, almost by instinct, often before any-one even noticed I was taking a photo... and if I needed to change any settings.. not that it had many, I was familiar enough with the thing, that often it would be focused by the time it reached my eye and any compensation' was dialled in, in a moment, if needed... it did not intrude on the activity, it did not become the activity; it was 'incidental' to my holiday.. and I have thousands of great memories it has captured.
You really do NOT want to be reading the instruction manual for the camera you hope to get all these great 'life moments' with, sat in the air-port concourse waiting for your flight to be announced; & you really don't want your holiday to be bogged down by 'interruption' for 'must have' photo-ops; that have you fumbling with menu's and cursing batteries NOT 'having a holiday'.
If you are familiar and comfy with your camera-phone... THAT might be as good as anything... it'll get you pictures, and probably not half bad ones, and yon can concentrate on enjoying the holiday.
Other wise? Well, whatever you might get... get it early, and get out and practice with the thing until using it is 'instinctive' and you don't have to 'fuss' to get a picture..