Perhaps a young predator is on a rite of passage and discovers a new planet that he decides could be a new home for his clan. He has to face various challenges on this planet, including native creatures that are as dangerous as the prey he's used to. Along the way, he might encounter some humans who are also exploring the planet, leading to an interesting dynamic between the three species.
You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own. These platforms have a wide range of fan - created works, including AVP fanfiction. Just use the search bar and type in 'A New Home AVP' to find relevant stories.
One possible plot could be a character moving into a new home that is rumored to be haunted. As they start to unpack and settle in, strange things begin to happen like objects moving on their own and cold spots in certain rooms. They then decide to investigate the history of the house to find out what's really going on.
Luke Skywalker could be one of the main characters. He might encounter an Alien for the first time and have to use his newfound Jedi skills to fight it off, or he could team up with a Predator who senses his potential in the Force.
Well, it could be about Harry moving into a magical cottage filled with strange and wonderful creatures. Maybe he discovers a hidden room in his new home that has ancient spells and potions.
Perhaps in this fanfiction, Kevin discovers a magical ability while being alone in New York. He can communicate with the pigeons, and they become his allies. The '967' could be some sort of frequency or signal that only he and the pigeons can understand, which helps him in his new adventure against the bad guys.
The plot could be that Dumbledore assigns Harry to clean Snape's home as a way to build a bond between them. Harry initially resents it but as he cleans, he finds a diary that reveals Snape's unrequited love for Lily. This discovery makes Harry see Snape in a new light and he decides to try and befriend him. He starts to clean with more care, and when Snape returns, he is initially angry but then realizes Harry has a newfound respect for him.
Maybe Harry Potter builds a home in a hidden forest near Hogwarts. He could use magic to create a cozy cottage with a fireplace that always has a warm fire burning, and rooms filled with memories of his friends and adventures.
Perhaps it's about one of the werewolves going back to their reservation. They might be reflecting on how their life has changed since the appearance of the vampires in the area. For example, Jacob could be on a trip home and thinking about his complex relationship with Bella and his pack.
One possibility could be that Alice and Harry return to their childhood home. They might find it full of old memories and start reminiscing about their past adventures there. Maybe they find an old treasure map hidden in the attic that leads them on a new adventure in the area around their home.
It could be a single mother and her young child. The mother is trying to start a new life for them in the new home, facing difficulties like finding a good school for the child and making enough money to pay the bills. The child, on the other hand, is excited about the new place and makes friends easily in the neighborhood, which in turn helps the mother to feel more at home.