Fischer attended the High School of Music and Art in New York City, where she became an accomplished classical pianist. She received a degree in political science from Cornell University before graduating from Columbia Law School in 1959. Fischer began her career as a lawyer practicing civil rights law, poverty law, and criminal law but in the early 1960s, she changed course and left the law to produce radio documentaries for the Canadian Broadcasting Corporation for whom she also covered the Israeli Six-Day War. In the early 1970s, she opened the New York City office of NPR, where she continued to produce radio features.