Cabfare from JFK to manhattan is $35, but that may be going up because the cab fares may be raised. Note there is no flat fee to the airport.
NYC has lots to do and it depends on what you are interested in. I've never done the helicopter. There used to be (and may still be) the circle line that is a boat that circumnavigates manhattan island. Very interesting. When I go back I'm only interested in the Pizza and Bagels.
Alan