Goldstein, born Rebecca Newberger, grew up in White Plains, New York. She was born into an Orthodox Jewish family. She has one older brother, who is an Orthodox rabbi, and a younger sister, Sarah Stern. An older sister, Mynda Barenholtz, died in 2001. She did her undergraduate work at City College of New York, UCLA, and Barnard College, where she graduated as valedictorian in 1972. After earning her Ph.D. from Princeton University, where she studied with Thomas Nagel and wrote a dissertation titled "Reduction, Realism and the Mind," she returned to Barnard as a professor of philosophy.