One of my favorite trips when I lived on Long Island was to Amagansett, one of the few LIRR stations with a very short platform. It is a short walk to downtown with several nice eateries and also a short walk to the Atlantic Shore Beach.
I lived in, actually went to graduate school in what was then SUNY at Stony Brook, now called Stony Brook University, so a trip to Montauk involved a Suffolk County Bus System bus ride to one of the stations on the South Shore Line of LIRR, something like Blue Point or Patchogue in those days, forty or so years back. After I baught a second hand car, an Audi 100LS, I seldom took LIRR to Maontaul or Hamptons from Stony Brook. Just drove there. After moving out of LI I have been to the Hamptons and Montauk many times by LIRR from NYP. Montauk has grown considerably aroud the train station since those days when there was literally nothing within miles of the station. Now there is a substantial restauran right opposite the station within a short walk, the last time I was there about 6 years back. Probably there is more now.