As the resident librarian on this forum, I would eagerly point out that with regard to libraries NYC offers a virtual treasure trove of all kinds of them, with all kinds of specializations, and virtually all of the highest quality.
Many of the specialty libraries in NYC are considered the equal of or even superior to many college libraries elsewhere in the country. (Another area where the Big Apple does things in a huge, grand style).
And so many of them are
open to the public, or charge a reasonable entrance fee, and offer not only books to read but also extraordinary art and cultural exhibits as well
The New York Public Library system (the branches along with the headquarters library) is easily one the best public library systems in the country. And its exhibits are always first rate
The Morgan Library (named of course for its founder, financier J. P. Morgan) is as much an art museum as a library, offering in addition to viewings of its iconic Gutenberg Bible exhibits of the first editions of prominent American and European authors, as well as displays on such diverse topics as the history of printing, literary trends, ethnic authors, and almost anything else one can imagine.
Here's an annotated list of some of the more prominent NYC Libraries one might consider visiting while in this remarkable city:
/theculturetrip.com/north-america/usa/new-york/articles/new-york-city-s-10-best-cultural-libraries/Of course going to see a library may not be the first thing that comes to mind when visiting NYC, but if you do get the chance to do so, you will likely find a lot more in that city's many wonderful libraries than just books.