Buttolph Collection of Menus at the New York Public Library contains largely American menus, many (but not all) from New York City; they are largely (but not entirely) from 1890-1910.
Schomburg Menu Collection at the New York Public Library's Schomburg Center for Research in Black Culture focuses on menus and food in the Black community.
W. Dieter Zander Menu Collection from the New York Public Library includes menus from around the world, collected during Zander's lifetime as a businessman and artist.