Question: What state is the location of this embayment off Long Island Sound that is the location of the Cornelius Van Wyck House?

Context paragraphs:
Van Wyck Junior High School: Van Wyck Junior High School (pronounced Van Wike) is an intermediate school in Hopewell Junction, New York, United States, located at 6 Hillside Lake Road and is a part of the Wappingers Central School District.  The school opened its doors in 1964 and presently teaches grades seven through eight.  New construction of homes in the area have led to overcrowding in Van Wyck and the district's other junior high, Wappingers Junior High School.  Incapacity led to the western-most wing (which runs north-south) to be added to the school, which now serves the sixth grade.  The extension is only noticeable in the new rooms which touch where the outside of the school once was: normal-sized bricks are seen on the eastern walls of those rooms, while the rest have walls made of cinder blocks.  In late 2004, modular classrooms were opened approximately 75 ft south of the existing building to accommodate some sixth-grade classes which the school could not hold.  The present principal is Steven Shuchat.

Douglaston Historic District: Douglaston Historic District is a national historic district in Douglaston, Queens, New York.  It includes 631 contributing buildings and three contributing sites on a mile-long peninsula extending into Little Neck Bay.  All but one of the buildings are in residential use and the majority were built in the early- to mid-20th century as a planned suburban community known as Douglas Manor.  In the early 20th century, the Rickert-Finlay Realty Company of Manhattan purchased 175 acre of the Douglas' family holdings, and formed the Douglas Manor Association, creating a planned community.  Many of the houses in this area were built in architectural styles popular at the time, such as Tudor, Mediterranean, Colonial Revival, and Arts and Crafts.  Located within the district are the separately listed Cornelius Van Wyck House (c. 1735) and Allen-Beville House (c. 1848-1850).  Another notable early building is the Van Zandt manor house (c. 1819), which is now the Douglaston Club.

Wilfrid Van Wyck: Wilfrid Van Wyck (16 November 1904 – 13 October 1983, in Woking, Surrey) was a British classical music artists impresario and manager through his agency, Wilfrid Van Wyck Ltd, based in London.  He was the second president of the European Association of Artist Managers.

Harbor Defenses of Long Island Sound: The Harbor Defenses of Long Island Sound was a United States Army Coast Artillery Corps harbor defense command.  It coordinated the coast defenses of Long Island Sound and Connecticut from 1895 to 1950, beginning with the Endicott program.  These included both coast artillery forts (all but two on islands in the sound) and underwater minefields.  The area defended included the approach via the Sound to New York City, the port cities and manufacturing centers of New London, New Haven, and Bridgeport, and eventually included the submarine base and shipyard in Groton.  The command originated circa 1900 as an Artillery District, was renamed Coast Defenses of Long Island Sound in 1913, and again renamed Harbor Defenses of Long Island Sound in 1925.

Cornelius Lawrence: Cornelius Van Wyck Lawrence (February 28, 1791 – February 20, 1861) was a politician from New York.  He became the first popularly elected Mayor of New York City after the law was changed in 1834.

Little Neck Bay: Little Neck Bay is an embayment in western Long Island, New York, off Long Island Sound.  Little Neck Bay forms the western boundary of the Great Neck Peninsula, the eastern boundary of which is Manhasset Bay.  The political boundary between Nassau County and the borough of Queens runs through the bay, bordering the neighborhoods of Douglaston/Little Neck.

Van Wyck, South Carolina: Van Wyck is a town in the panhandle of Lancaster County, South Carolina, United States.  The name "Van Wyck" comes from a Dutch habitational name for someone from any of the many places in the Netherlands named Wijk, from the Dutch word "wijk", meaning "district" or "settlement".  There are several ways of pronouncing the name of the community—"Van Wick", "Van Wack", and "Van Wike".  Families who have lived in the area since its founding in the 1880s generally pronounce it "Van Wack".  On August 15, 2017, the residents of the community voted to incorporate it as a town.

Jamaica–Van Wyck (IND Archer Avenue Line): Jamaica–Van Wyck ( ) is a station on the IND Archer Avenue Line of the New York City Subway, located on the west side of the Van Wyck Expressway between Metropolitan Avenue and 89th Avenue in Richmond Hill, Queens.  It is served by the E train at all times.

Briarwood (IND Queens Boulevard Line): Briarwood (formerly Briarwood–Van Wyck Boulevard or Van Wyck Boulevard) is a local station on the IND Queens Boulevard Line of the New York City Subway.  Located at the intersection of 84th Drive, Main Street, Queens Boulevard, and the Van Wyck Expressway, in Briarwood, Queens, bordering Kew Gardens, it is served by the F at all times and the E at all times except rush hours and middays.

Cornelius Van Wyck House: The Cornelius Van Wyck House is an 18th-century Dutch Colonial home located on the shore of Little Neck Bay in the Douglaston section of Queens in New York City.  This house overlooks Little Neck Bay and is well known for both its age and architecture, and especially for its original owners.  It was designated as a landmark by the New York City Landmarks Preservation Commission in 1966 and added to the National Register of Historic Places in 1983.  The Cornelius Van Wyck House is considered to be the "most impressive architectural remnant of the early Dutch Culture" in New York.

Supporting paragraphs: Cornelius Van Wyck House Little Neck Bay
Answer: New York