Draper's work as a historian of the Cuban Revolution brought him to the attention of the Hoover Institution on War, Revolution, and Peace, an anti-communist think tank located at Stanford University. Draper accepted a Hoover Institution fellowship and remained there until 1968, at which time he departed, ill at ease with the growing conservatism of the institution. Draper moved across country to accept a similar post at the Institute for Advanced Study located at Princeton University, where he focused his scholarship on the question of race relations.