Many large libraries provide funding to use their collections, often as part of outreach associated with their Title VI center. Knowledge of a collection's strengths is useful in selecting a library to visit; some libraries have divided collection responsibilities with sister institutions and an understanding of these cooperative agreements will minimize your chances of a wasted trip. Contacting the Japanese Studies librarian before you go is the best way to ensure a productive trip. 

Libraries which have often provided travel grants to use their collections

Chicago, Center for East Asian Studies

Duke, East Asian Collection 

Harvard, Harvard-Yenching Library 

Kansas, East Asian Library

Library of Congress: Mellon Fellowships
In addition to the requirements of U.S. citizenship or permanent residency and possession of a doctoral degree, the awards are for scholars who are proposing or working on a second major research project with a focus on foreign-language material.

Michigan, Center for Japanese Studies

Pittsburgh, East Asian Library 

Princeton, Friends of the Princeton University Library Visiting Fellowships

Stanford,  The East Asian Library

Washington,  East Asia Library

Independent Sources of Support

Northeast Asia Council, AAS

Japan Foundation