Penny's friendship with the whole gang is a great storyline. She is often the bridge between the nerdy guys and the more 'normal' world. For example, she helps them with social situations and they, in turn, help her with things like knowledge and different perspectives.
There are no such inappropriate stories in the official plot of 'The Big Bang Theory'. The show mainly focuses on the nerdy and humorous interactions among the characters, their friendship, and their romantic relationships in a family - friendly way.
One common theme is the growth of their relationship. Their friendship or potential romantic relationship evolving over time, with Penny helping Sheldon become more social and Sheldon introducing Penny to new intellectual concepts.
There might be a fanfiction where Penny is pregnant and she starts to feel really isolated because she's the only one in the group going through this. She misses her old life a bit, and the story could be about how she overcomes these feelings with the support of her friends and Leonard. It's very emotional as it deals with her internal struggles.
One appropriate topic could be their adventures in scientific experiments together. For example, they could be collaborating on a project where Penny's practical skills and Sheldon's theoretical knowledge combine in a comical yet productive way.
There could be a fanfiction where Penny's pregnancy makes Leonard super nervous. He starts freaking out about being a dad and all the responsibilities. Meanwhile, the rest of the gang tries to support them in their own clumsy ways. It's interesting to see how the characters' relationships develop during this big life change.
Their ability to grow together is another positive. At the start, they had some differences but as the series progressed, they became closer and more understanding of each other. They learned from each other's strengths and weaknesses, which is a great example of a healthy relationship.
Another great one is 'Sheldon and Penny: Unlikely Friends'. In this fanfic, it focuses on the early days of their relationship when they were just starting to get to know each other. It details their initial misunderstandings, like when Sheldon didn't understand Penny's pop - culture references and how Penny found Sheldon's scientific rants both annoying and fascinating at the same time. As the story progresses, they start to form a unique bond that is different from Sheldon's relationships with the guys.
One interesting story is when they first met through their mutual friends in the group. Penny was initially a bit more outgoing and worldly compared to Bernadette, but they quickly found common ground in their love for their partners and their shared experiences as women in a group dominated by male scientists. For example, they often teamed up to give advice to Sheldon when he was being particularly difficult in his relationships.