The New York Public Library (NYPL) has 88 neighborhood branches in the Bronx, Manhattan, and Staten Island, as well as four scholarly research libraries. You can ask for a book to be sent to a branch that is convenient to you, and return your books to any branch.
Now (starting July 2018) you can use your library card from the New York Public Library, or the Brooklyn Public Library, or the Queens Public Library, to gain FREE entrance into a wide range of museums and other cultural institutions through Culture Pass ! You do have to make a reservation online.
See the Culture Pass website for more details.
To see all the NYPL branches, click here.
The Schomburg Center for Research in Black Culture is one of NYPL's four research libraries, and has valuable special collections.
It is usually open later than other branches, and also holds many interesting public events. It's only one subway stop away from Hostos on the downtown 2 train, near the subway exit at 135th Street.
Just a few stops north of Hostos (near Fordham Road), the Bronx Library Center is the biggest NYPL branch in the Bronx. It is also usually open later than other branches, and has free public performances and many free classes.