In some fanfictions, they might travel together. Harry, with his love for adventure, and Ginny, being equally brave, could explore new magical places. They might go on a quest to find a long - lost magical artifact and along the way, face various challenges and strengthen their bond.
One possible scenario could be them renovating their home at the Burrow. They might be adding new rooms for their future family. Ginny could be using her magic to make the place more cozy while Harry helps with the physical labor, like moving furniture with a levitation charm.
Another aspect could be their social life. They would likely be very involved in the wizarding community. They could host parties at their place where all their friends from Hogwarts come over. Ginny would be the life of the party, and Harry would enjoy seeing his friends having a good time in a more peaceful post - Voldemort era.
One possible scenario could be that they have a peaceful family life. They might raise their children in the wizarding world, teaching them about magic and the values of love and courage. Harry could be involved in the Ministry of Magic, perhaps working on improving the safety and equality in the wizarding community. Ginny, on the other hand, might continue her career as a Quidditch player or become a Quidditch coach, passing on her skills and passion for the sport.
Maybe they go to a wizarding cottage in the countryside. They explore the nearby magical forests together, discover new magical creatures, and Ginny could teach Harry some new Quidditch tricks in the large open fields around the cottage. And of course, they have cozy evenings inside, cooking together and snuggling up by the fireplace.
Another possibility is that they would take a stroll in the moonlight around their new home. They would hold hands and reminisce about their adventures at Hogwarts. Harry might tell Ginny how much he loves her all over again, and Ginny would respond with sweet kisses, and then they would go back inside to have a warm drink and cuddle by the fireplace.
They might get married and start a family right away. In fanfiction, it's common to see them settling down and having kids, living a peaceful life after all the chaos of the battle.
One interesting scenario could be them renovating their home at the Burrow. Harry might use his magic to make some unique changes, like creating a hidden room for his memories of his parents. Ginny could be in charge of decorating, adding a Quidditch - themed corner. Another could be their travels. They might visit different wizarding communities around the world, learning new spells and making new friends.
In some fanfictions, it might occur during a trip on the Hogwarts Express. They are sitting in a compartment, just the two of them. The train is chugging along, and the scenery outside is passing by. Harry looks at Ginny and starts a conversation about their future. Then he casually asks if she would like to go on a date with him when they get back to Hogwarts. It could also be after Ginny has been in some sort of danger. Harry is so relieved when she's okay that he blurts out his feelings and asks her out.
It could also be a moment of affection during a celebration. For instance, after Gryffindor wins a Quidditch match. Ginny, being excited and proud, jumps on Harry's lap in the middle of the celebration in the common room. They would be laughing, sharing the joy of the victory, and perhaps stealing a quick kiss or two.
Another scenario could be them working in the field of magical creature conservation. They might team up to save an endangered species. Harry's experience with magical creatures like Buckbeak and Ginny's love for all things magical could lead them to create a sanctuary or a breeding program for the creatures.
One possible scenario could be that Ginny meets an old acquaintance who has changed a great deal and she starts to have feelings for this person while still being with Harry. Maybe they share a common interest that she feels Harry doesn't understand. However, this goes against Ginny's strong character in the original series, so it's a very different take in fanfiction.
In some versions, it could be that Harry has to die to break a dark curse placed on Ginny. He discovers that his life is the key to saving her and willingly gives it up. He might have a premonition about Ginny's fate and decides that his death is the only way to change it. He then confronts the source of the curse and allows it to take his life instead of Ginny's.