Best and fastest way from JFK to Main St. Flushing

Hi, We are two Delta Flight Attendants who will be commuting to NYC and thinking about staying in Flushing near the Botanical Gardens to save $$$ when we're in NY. What would be the approximate taxi fare to JFK? We are figuring that if we take the Air Tran to the F to the 7 and then walk, for $14 (both) it might be about the same for a a cab?

Any suggestions for a car service?