The following are two books about teenagers that run away from their parents and end on a positive note. Both books feature female characters who find success living amongst difficult situations and enter into alternative family units. I read these books several years back and this is what I remember about them. If you are interested in this subject, I'd recommend them both!
Looking for Home by Jean Ferris (1989)
Soon after her prom night, 17 -year-old Daphne realizes she is pregnant. When her boyfriend goes off to college, she fears telling her parents the truth. She hops a bus to a new city and finds a job as a waitress. The owner and some of the customers take a special interest in Daphne, forming an alternative family and a support system for this brave girl.
To Take A Dare by Crescent Dragonwagon (1982) w/ Paul Zindel
This novel is based on Crescent Dragonwagon's own experiences. She wrote the book with Paul Zindel (whose editor, Charlottte Zolotow was also Crescent's mother). Chrysta runs away from her parents and the book follows her adventures thumbing it on the road. After suffering from some degree of loneliness, she ends up working at a hotel in Excelsior Springs, Arkansas, a hippy town in the Ozark Mountains. There she finds a boyfriend and learns what it means to love and be cared for. Dare is the name of a young boy who lives in the town that's far more lost than Chrysta. As she matures, she learns to help him and to take care of herself.