One place that I know of that has lots of coastal rocks is Lloyd Neck, Caumsett State Park. Other spots along the north shore will have rocks as well, all the way out to the Peconics and Montauk.
The high headland and bluff indicate that this is not a south shore beach, most of which are quite flat in terrain. Not that this will help much but I'd guess this scene was somewhere between Port Jeff and Mattituck. Port Jeff has a pretty tall head land. A lot can change over 130 years though.
"The cure for anything is salt water~ sweat, tears, or the sea." ~Isak Denesen
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