Two library buildings exist in my immediate neighborhood just a block a way from one another.
This branch of the New York Free Circulating Library opened in 1898. You can read more about the Free Circulating Library here. I believe that the Free Circulating library system got absorbed by the NYPL. For most of my time living in the neighborhood this library building had been used by a Ukrainian association. It seems to have a new owner and the building looks like it is in much better shape than it has been for the past few decades.
The library in actual use in the neighborhood is this one.
A not particularly wonderful example of New York City mid twentieth century civic architecture. The blocks between Columbus and Amsterdam Avenues in the 90's and low 100's were filled with gangs during the post WWII era. Many of the brownstones and small apartment buildings had not survived the Depression particularly well. Rather than deal with both issues in a small way, the city knocked down the older buildings and put up new housing. Some of it is low income housing and some is middle class housing. The centers of the blocks usually have clusters of civic buildings. Next to the library is a health center. Across the street there is a police station and a fire house. Other blocks have other civic institutions, tucked in among the tall apartment houses.
I am quite fond of this library. It's not all that beautiful but it is filled with fond memories for me and for my kids.