Make sure you check the opening hours / days of the museums if they're key for you, as lots shut on 1-2 days of the week, and around 5/6pm.
Don't forget to tip properly even in bars - $1 for a beer / easy drink, $2 upwards for a complicated cocktail thing. Brits are renowned for not tipping and being tight. Also, tip well on a first round and you'll find a measure of spirits is twice the size of a normal one
if you want to splash the cash, there's some really really nice restaurants. Lots of them (Daniel, cafe boulud etc) often do set price tasting menus. My favorite tapas place (michelin star) is called cafe mono just down by union square
Beware for shit coffee - the yanks love buckets of the flavored stuff which is rank. if you can, find a Fika branch (Swedish and 4-5 places round the city) or Financier (a French place with outlets dotted around)
I'm going to be controversial and say little italy isn't worth it as its so small now (reduced to 1-2 streets) and not a lot going on in chinatown tbh altho my friend came and bought a v good replica handbag there
Download the subway app which will provide up to the minute info on outages etc as the paper maps are shit beyond extreme and v confusing! Subway lines usually run an express and local on the same lines, which means you can often miss your stop if you get on the wrong one (express tends to jump many stations)
Sort out your mobile data roaming charges before you arrive - data charges here are eye watering and it can be difficult to access public wifi, altho its becoming more available. in my experience standard hotels will try and rinse you $25 a day for wifi in the rooms
Times square is an armpit and I wouldn't make my worst enemy go there - I usually send in guests with directions and that Ill meet them 2 hours later. It's like piccadilly circus on steroids with nothing actually 'there' if that makes sense? Unless you want to visit consumer laden stuff like the M&M store. they do have a theatre ticket outlet there tho that you can snag v discounted tickets for big shows from
Probably worth noting also - check schedules and opening times generally for stuff as you're there over easter and Passover. We don't get Good Friday or easter Monday off, but easter and passover is massively observed so does affect stuff over the Friday - Monday