As a child, Daryl was very shy and was diagnosed as 'borderline autistic'. Overcoming this, she graduated from the University of Southern California's School of Theatre, practiced ballet with Maria Tallchief, studied drama at Chicago's Goodman Theatre, and also played keyboard and was a backing singer for Jackson Browne. Her movie career took off in a big way after Blade Runner.

Daryl's younger sister Page Hannah (born 1964) is also a successful screen actress.

Daryl lived with John Kennedy Jr. for several years. It is said that the late Jacqueline Kennedy Onassis was strongly against her son marrying an actress.