You can also take a Babylon train and connect to the Montauk line to Sayville and take the S57 bus. There is also a bus called Hampton Jitney but it stops on the east side of Manhattan. You can take either the 8th Avenue Local or express subway to either Penn station or sutphin boulevard archer avenue jfk station which connects to the Jamaica Station or 7th avenue or any other subway line except the grand central shuttle to Atlantic Terminal in Brooklyn, Woodside Station, Forest Hills Station or Kew gardens station in queens and take either the long island rail road Babylon line to Babylon and connect to the Montauk line to Sayville or take the Ronkonkoma line to Ronkonkoma and take the S57 Suffolk county transportation bus to the airport
From times square you can take the 1, 2, or 3 train (about 5 minute ride) to Penn station (or walk) then get on a Ronkonkoma train to the last stop, Ronkonkoma (which is at the airport but on the opposite side of the passenger terminal). From here you can take an Uber, bus, or cab to the passenger terminal(about 5 minute ride). *The train from Penn to Ronkonkoma can take anywhere from 66 minutes to 86 minutes depending on what type of train you catch. Schedules can be found on the MTA website.
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