The largest library in New York and the second largest one in the US (the first one being the Library of Congress). It is home to more than 50 million items (mainly books but also DVDs, CDs, etc.) and its collection covers every possible topic that has ever been written about.
The New York Public Library is also a popular filming location. If you are a fan of Ghostbusters, you will certainly remember the scenes filmed there. Among other films that feature the library are: Breakfast at Tiffany’s, Sex and the City or Spider-Man.
You can enter the library for free (even the Beaux Arts building itself is definitely worth seeing) but be aware that you are entering not only an important sight but also an actual library so you are expected to behave accordingly.