I wanted to make a note on the subject of the A train through Queens and Brooklyn. Some people may recall that the MTA used to run (until 1989 or so) a special express train with no stops except in Manhattan and at JFK along the A train tracks. It eliminated some of the concern of danger at the local subway stops, but it still required connection to the terminal bus in a remote JFK parking lot.

New York's easiest connection to any airport is probably via the Jamaica Queens station - a short and inexpensive cab or bus ride from LGA and from JFK. And frequent LIRR trains into Penn Station.

Unfortunately, none of the three airports have truly unimodal public transit links to the city. Usually, taxis are the way to go, but you have to know your bridge and tunnel options in advance.