The selected list of Cultural Facilities that you will need to research are all well-known New York buildings or were designed by notable architects.
To find information on these buildings, you can search the Library's catalog Bobcat by the name of the institution, architect, or building.
You can also search for the building or architect on the verified web resource greatbuildings.com. Great Buildings is a digital compendium of images, plans, and information about notable buildings and architects, provided by Architecture Week, a publication. This is a fabulous source that provides further sources on each page about that work of architecture.
It is also possible the building is landmarked, in which case you can visit the Neighborhood Preservation Center, a non-profit which provides a database of Designation Reports. These detail the history and design of the building. In this case, you will want to search for the name of the building as a Keyword search. Make sure you have all alternate building names, as these can change over time.