The following museums are always free:
Hebrew Union College—Jewish Institute of Religion
The Hispanic Society of America
Jeffrey’s on Essex @ the Essex Street Market: Cuchifritos Art Gallery
The Museum of American Illustration at the Society of Illustrators
The New York Public Library: Humanities and Social Sciences Library
The New York Public Library: Library for the Performing Arts
The New York Public Library: Science, Industry and Business Library
Scandinavia House—The Nordic Center in America
Schomburg Center for Research in Black Culture
Statue of Liberty & Ellis Island Immigration Museum
The Smithsonian Museum of the American Indian at NY Customs House is free.