Lilith

Locust Valley (aerial view) includes neighboring Lattingtown (Locust Valley is the P.O., likely accounting for an occassional discrepancy in the filming location)

Set in a private mental institution (Chestnut Lodge), it tells of a trainee occupational therapist Vincent Bruce (Beatty) who becomes dangerously obsessed with a seductive, very able, schizophrenic patient Lilith Arthur (Seberg). Chestnut Lodge (located in Rockville, Maryland) would not permit filming on location so those scenes were done in a vacant mansion rented by the production company, Centur Productions, on the North Shore of Long Island (Locust Valley). ~ Wikipedia

The probable filming location for Poplar Lodge is Killingworth [ref] – last paragraph for reference

Of Interest:

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It was director Robert Rossen’s final film before his death in early-1966.