If you're uncomfortable driving through New York City to get to Long Island, you may be able to reach the island by taking the vehicle ferry from Bridgeport, Connecticut to Port Jefferson, NY. Route 112 then crosses Long Island to Patchogue, usually less than an hour's drive south.
The
Cross Sound Ferry links New London, CT with Orient Point, NY, on the easternmost end of Long Island. Allow at least 2 hours to drive from Orient Point to Patchogue or Sayville.