​I found this information from other hunters:

• Many think this clue refers to the Queen Anne style of building and architecture.

• This building is the Town of Liberty Government Center, and the backyard of Hillig’s store backs up to this building! This building that everyone refers to is actually not Queen Anne style of architecture 

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Information I have found myself:

• Queen Ann had granted the Hardenbergh patent to "promote the settlement of the country. The immense estate had not been divided between the original proprietors or their heirs and legal representatives, until the company, from its numbers, had become too unwieldy for practical purposes. A partition then took place; and it was subsequently subdivided by heirs and assigns, who were scattered far and wide over the earth's surface. Hence the people of small means who would have purchased farm-lots in that part of the patent situated in Sullivan, knew not whom to apply to, except in a very few instances. One of these exceptions was a Captain Charles Brodhead, who lived in Ulster county, on the road which led to the Great Lot in Neversink and Rockland inherited by Livingston. He (Brodhead) owned the "8,000 acre tract" in Liberty, which had descended to him from the Brodhead who purchased of Hardenbergh, the patentee. Charles Brodhead's residence and ownership led to the settlement of Liberty.     http://genealogytrails.com/ny/sullivan/history_liberty.html

• I found that the Government bldg. in Liberty that everyone believes to be Queen Anne style of architecture was actually the Keller House, 120 North Main Street, and is a fine example of Downing-inspired Gothic Revival architecture, and was built in the mid-nineteenth century 

• The Queen's back yard could be a general reference to all the land that Liberty sits on, being owned by the Queen at one point.

• 27 Saint Pauls Pl, Liberty, NY 12754 is the Queen Anne House