Sometimes they meet in a more mundane place, like a coffee shop in the Muggle world. It could be a serendipitous encounter where they recognize each other after years apart.
Often, they meet at a magical event or gathering. Maybe it's a wizarding conference or a charity function for magical causes. Such settings provide a natural backdrop for their reunion.
It could be at a school reunion. Maybe they bump into each other by chance when visiting Hogwarts.
Harry could develop a more peaceful side to his personality. He's seen enough death and destruction, so he focuses on promoting harmony in the wizarding world. Hermione may change in her approach to magic. Instead of just relying on book knowledge, she starts to experiment more, using her creativity. This change in their personalities can lead to new adventures and a different kind of relationship between them in fanfiction, whether it's a stronger friendship, a romantic relationship, or a partnership in making the wizarding world better.
It could be that they were both looking for a place to unwind after a stressful day and ended up in the same bar. Or perhaps they were invited by mutual friends and that's how they crossed paths.
One possible plot could be that after the war, Harry and Hermione realize they have a deep bond that goes beyond friendship. They start to rebuild Hogwarts together and in the process, their feelings grow. They get married in a small ceremony at Hogwarts with their closest friends in attendance.
He'll most likely meet Bella Swan. Maybe he stumbles upon her in the forest and she's initially very wary of him, but then they start to talk and find they have some similarities in terms of being outsiders in their own worlds. He could also meet the Cullens. Edward might be intrigued by Harry's magic and Harry could be fascinated by Edward's vampire abilities.
Perhaps Harry meets magical creatures that are rarely seen by wizards. Since he is out exploring after the war, he might stumble upon a group of centaurs who have their own unique wisdom about magic and the future. He could also encounter veelas, and through his interactions with them, learn more about the different cultures within the magical world. There's also a chance he meets other young wizards who are on their own adventures, and they form a sort of traveling group together.
It could be that Harry Styles is lost on campus and Louis offers to help him find his way. Or perhaps they both attend a lecture and end up sitting next to each other and start chatting.
It could be in a class they both have, or maybe at a campus event. Depends on the author's imagination!
It depends on the specific fanfiction. Some might show them having a bit of a rough start. For example, Ginny could be angry that Harry distanced himself during the war for her protection. But then they would talk it out, and realize that they both still love each other deeply. From there, they would start to work on their relationship. They might go on adventures together, rediscover their shared interests, and their relationship would progress as they create new memories together after the war.
They might share a very emotional moment. Harry could finally let go of all the war - related stress and just be himself with Ginny. He might tell her about all the things he couldn't during the war, like his real fears and hopes for the future. And Ginny would be there for him, comforting him and showing her love in a more peaceful and free environment.
One possibility is that they form an unlikely alliance. Maybe they start sharing their different skills and knowledge. For example, the Winchesters could teach Harry about hunting supernatural creatures in their way, while Harry could introduce some of his magic to them. They might also compare their experiences of facing great evils. The Winchesters have fought demons and angels gone bad, and Harry has battled Voldemort and his Death Eaters. It could be really interesting to see how they react to each other's stories.