Go to the AirTrain site, you get on AirTrain without paying but it costs $5 at the Jamiaca Station, but if you put in $7 you get $2 additional on the ticket for the subway.
The AirTrain is great couple of stops and viola, right at the subway. I take E train subway and the great thing is it stops at Lexington and 52nd or 53rd and then at 5th and then at 8th.
Reason I mention that is those last two stops are theater, Rockefeller and Times Sqaure area and it's a great popping up point.
Trouble as MasterBlaster alludes, it takes about 30 or more stops on the way in. Long time but even taxis hit traffic and especially at about 7AM when you will be exiting the airport.
Subway will be crowded. But expect the taxi to cost lots of money due to idling in traffic. $55-60 is min from my experiences.
Seems a toss up. In a taxi as MB says, at least you see NYC.