I got a taxi in when I went to NY (came in from Newark though). We were given an agreed price in advance in a very well organised yellow cab queue by a taxi marshall before even getting into the cab.
We had to pay the toll to get into NYS (not a problem with JFK I assume) and then gave what we thought was a generous tip but were quite bluntly told he didn't think that was enough.
Tipping culture is huge if you haven't been before. Watch the hotel staff circle to move in to grab your bags, be wary, few will do anything without a tip, they make up often poor wages from tips which are pretty standard there, so if you aren't prepared to tip then DIY.
Keep a supply of low value currency on you for tipping purposes to try to give whole what you want to tip and get to grips with how much you are expected to tip where (doubtless you will be told if you don't so good to wise up beforehand).
Have a great time, New York is an amazing place and lots of previous questions on here with suggestions for all kinds of things from things to do and see to tipping culture.
We found a great diner for breakfast each morning called the Red Flame, not too far from Time Square. Very New York, good food and decent prices and quick service.