Penny lives with her mom, Pam, in a little trailer by the river. While Pam is out carousing at the saloon, Penny quietly tends to her chores in the dim, stuffy room she is forced to call home. She is shy and modest, without any grand ambitions for life other than settling in and starting a family. She likes to cook (although her skills are questionable) and read books from the local library.

Source - Stardew Valley Dev Update #12

Penny lives with her mother Pam. She's friends with Maru and Sam.

She also teaches the local children, Jas and Vincent, at the museum a few days a week and accompanies them to the playground sometimes.

During the eight-heart cutscene, Vincent remarks that he once saw Sam and Penny climbing trees, at which Penny becomes visibly startled and scolds Vincent for gossiping. Concerned has explained that he "wasn't trying to imply anything serious" with the scene regarding a continuation of Penny's interest in Sam. "[At 8 hearts,] she's not actually interested in Sam any more."

Source - Stardew Valley Wiki