Taxi ride is $45 (flat rate) from JFK -and that does not include tip and tolls.
You could also take public transportation (bus to subway, airtrain to subway, etc) and that can range from $2 to about $12 depending on which service you use:
With public transportation. once you get out of the airport, you have two choices:
1. a city bus ($2), or
2. the airtrain ($5)
And then, you HAVE to transfer to:
1. the city subway ($2 -you get a free transfer from bus to subway with the city fare card aka Metrocard)
2. the commuter railroad or LIRR ($5 to $7 -depending on the day/time. note: add another $5 if you don't buy tix at the train station)
There is also another alternative at the airport,
if you're going to the Grand Central/Times Square areas and hotels in the midtown area only. You can take a shuttle bus. Fare is $15 one way and you wouldn't have to deal with transferring from bus to subway etc etc. For more info, you can go to this website http://www.nyairportservice.com/
And last but not least, there are two other shuttle services which are basically door to door service. You may have to call them and ask them about price because it varies depending on the destination.
1. Airlink New York (takes you to any location between 23rd & 63rd Streets) - 800-498-9676
2. SuperShuttle Manhattan (takes you to any location between Battery Park and 227th Street -including all hotels) - 800-258-3826
If you need additional info, you can always go to the airport website