One idea could be a story where they meet in a small, artsy town. Alexandra could be an artist painting a landscape when Logan, a wandering writer, stumbles upon her. They start chatting and find out they have a shared love for creativity and the simple things in life. This could lead to a budding romance as they explore the town together and inspire each other's work.
A plot could be that they are neighbors in a big city. They keep running into each other in the elevator or at the local coffee shop. At first, they just exchange pleasantries, but then one day, Alexandra's cat runs away and Logan helps her look for it. This event brings them closer and they start to realize they have feelings for each other.
You can start by looking on fanfiction.net. There are often a plethora of stories there. Also, Archive of Our Own (AO3) is a great place. Writers from all over post their fanfics there, and it has a wide range of works related to various fandoms, including those about Logan Lerman and Alexandra Daddario.
One popular theme is adventure. Given their roles in movies that often involve action and exploration, many fanfics will put their characters in new, exciting adventures. For example, they might be on a quest to find a lost treasure.
At first, their relationship could be strained. Logan may be scared by the news, and Rory might feel let down by his initial reaction. But as time goes on, they realize they love each other and want to make it work. They start going to prenatal classes together, and through this shared experience, they rekindle their love and build a stronger bond for the future.