The author never says exactly why Stargirl and her family moved. He leaves that to the reader's imagination. She and Leo had broken up, so it makes sense that she did not tell him that they were leaving or where they were going. From comments Archie makes, he knew that she was leaving and has a general idea of where she has gone. She has asked Archie to deliver "The Early Life of Peter Sinkowitz" to his parents. We also know that Stargirl has continued to be aware of where Leo is and what he is doing through the fact he receives a porcupine tie about a month before his birthday, fifteen years after the story takes place.
By leaving things hanging, as Jerry Spinelli did, he was able to write a sequel, Love Stargirl. The sequel begins with letters Stargirl is writing to Leo, her "once (and future?) boyfriend."