The New York Public Library's main branch is magnificent, and it's free, supported by contributions and endowments. A magnificent building, containing important collections on every area of research. Helpful librarians do the searching for you and bring books to you where you can search through them in quiet comfort and good lighting. Don't think of it as a lending library; it's a place to learn. The very atmosphere makes me feel privileged to be there.
New York Public Library - New York, NY is recommended by maddy