As a youngster growing up in Brooklyn, I went with my father and mother, who were a union welder and bank clerk, respectively, and four sibs to some cottages near Montauk Point for 15-day vacations every year. We'd spend time at Sag Harbor and the Hamptons to visit the museums and beaches.
35 years later, when I moved back to NY, I would look forward to catching the LIRR to Amagannsett, Montauk, East Hampton or South Hampton.
These towns are nice because they are remote, historic and scenic, not ticky-tacky beach towns. A large part of the beauty of their beaches is that their beach dunes are preserved much as they would have looked had they never been discovered. Enjoy them for what they are, but keep development back in NYC.
Pros: classy towns, clean beaches, LIRR accessible
Cons: , long trip from NYC, Oriented to locals
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