A 19-year-old Brooklynite, Libby Tucker is visiting her dead grandma’s grave at a New York cemetery, and reveals that she is moving to Hollywood to become an actress and find her father, screenwriter Herbert Tucker. Libby takes a bus to Denver, then hitchhikes the rest of the way. She tries to call Herb, but gets nervous and hangs up.
The next morning, Libby goes to the house where Herb lives and meets his girlfriend, Steffy Blondell, who invites Libby inside. After becoming acquainted and learning the reason why Libby is in town, Steffy decides to leave. Herb awakens to find Libby after a 16-year gap in their lives. The two chat about their pasts, and Libby fills Herb in on the family he left behind, including her younger brother Robbie. The two eventually begin arguing about Libby’s goal of becoming an actress. Just as Steffy returns, Libby runs out of the house.
Herb tracks down Libby at a motel and eventually persuades her to come back to live at his house. They begin to get along, although the high-strung Libby also begins to realize that Herb is not nearly as successful in Hollywood as she had assumed he was. He is also on the verge of losing Steffy, who has been asked on a date by another man and has been waiting a long time for Herb to make a commitment.
A studio makeup artist, Steffy helps Libby out by arranging for her go to a drama school. Libby meets a young man named Gordon there and together they take a part-time job doing valet parking at a celebrity-filled private party. Libby comes home at 3 a.m. and tells Herb about putting business cards on car windshields reading “Sunset Valet Parking. No party is too big or too small” on the front and “Libby Tucker, New York-Trained Actress. No part is too big or too small” on the back with her phone number included. Herb tells her that there is no chance of this helping her to become an actress, but Libby clings to her optimistic dreams.
Libby realizes more and more that her trip’s true purpose was to reestablish a relationship with her father. She decides to return home. After packing up, Libby makes a long-distance phone call to her mom and gets Herbert to talk to her for the first time in 16 years. He speaks with her brother Robbie as well. Libby goes back home after taking Herb’s picture for a keepsake. On the bus, she waves goodbye to Herb and Steffy, who appear to have worked out their differences.