The Mid-Manhattan Library, at 40th Street and Fifth Avenue, is the main language-learning repository of the New York Public Library. I used it a lot in 2009 and 2010, mostly for Pimsleur audio lessons, but also borrowed books and other resources as well. 

They have dictionaries, audio lessons (including Pimsleur CDs and VocabuLearn), grammar books, foreign films, and many foreign-language books, both fiction and non-fiction. (They do not have Rosetta Stone, except for English, nor do any libraries, as far as I know.) One can get a lot of great stuff at the New York Public Library without having to pay a cent. 

I stopped using the library for language resources at a certain point, simply because I realized I really needed to keep all my resources (and mark them up heavily), but it is worth checking out, particularly if you are on a language-learning budget.

To make life more convenient, you can go online and request that the materials you want be sent from Mid-Manhattan, which has the majority of the language materials, to your local Manhattan, Bronx, or Staten Island branch, and then return the borrowed materials to that same local branch when you are done. It’s very convenient if you live and work far from midtown! (Queens and Brooklyn have their own, separate library systems.)

One caveat: you may not always get the latest and greatest versions of things. Several years ago I got an old, defunct version of Pimsleur Arabic that caused me real problems until I consulted the publisher of Pimsleur directly and they figured out what the problem was.

The only reason I am not giving the library a perfect rating is that if your goal is language learning, you may face challenges getting what you want, since there is considerable competiition for popular resources. You can end up on a waiting list, so plan ahead and be patient.

Still, free is good!