Eastman was born in Oberlin, Ohio and moved to Cleveland at age 7. In her biography of her friend and mentor, William Howard Brett, Eastman wrote about an early interaction she had with him that would shape her career. Visiting the Cleveland library to acquire a book she needed for school, Eastman was told by an assistant that the book had been checked out and was unavailable. Brett, who was then head librarian, happened to pass by and overheard this exchange, and immediately offered to have someone go purchase another copy of the book for Eastman to check out. Following high school Eastman became a teacher, but soon decided to pursue library work instead.