Lindenwood Village was a 2,400-unit coop apartment development completed by General Builders in 1959-1960. "Electra-Rama" kitchens included a Westinghouse Appliance Center. Click to enlarge.

While the Linden Woods Swim Club seems to have vanished without an online trace, the only Google hits being to this and other photos, based on its name I would imagine that it was located in the sub-district of Howard Beach known as Lindenwood. Lindenwood is to the north of the Belt Parkway, with the main part of Howard Beach to the south. It takes its name from the major roadway Linden Boulevard that marks its northern border.

The apartment building in the left background appears to be one of the many similar buildings which comprise much of the eastern and southern ends of Lindenwood, the octagonal stairway window being a major clue. That would place the swim club in the semicircular area in the middle of Lindenwood, bounded by 151st Avenue, 153rd Avenue and 84th Street, which since the middle 1960's has been occupied by the 25 or so multistory buildings known as the Greenwood Arms Co-Operative.