It's been 4 years since I was last in NYC, but I've always taken the Port Authority (?) bus to either JFK (about $12 pp) or LGA (about $8 pp) from its location just across 42nd street from Grand Central Station by Park Avenue. Time it takes is about 1 - 1.15 hours to JFK, and 45 minutes to LGA, and the bus makes all the stops to the various terminals. Don't know if this service is still there, but I would guess so since I have been doing this for well over 20 years . From the airport, it's the same in reverse.

This method is very convenient if one is staying at the Grand Hyatt or nearby walking distance hotels, and you don't have a whole lot of luggage.