you can take the airtrain to jamaica station.from there you can either walk to LIRR and take the train straight into Penn station in NYC (i think it costs about 4 dollars, but it is fast) OR you can go to Sutphin Blvd/Archer Ave and take the subway into the city. The subway would take longer, but it is only 2 dollars per ride. Overall, it is very easy to get to the city if you have time.
you can take the airtrain to