He could meet other famous wizards from different countries. For example, he might run into Nicolas Flamel, who has been traveling around the world. Flamel could share with Harry some of his vast knowledge of alchemy and magic that has been passed down through the ages. This encounter could give Harry new insights into magic and its potential uses.
One possible plotline could be that Harry, traumatized by the events related to Azakaban, decides to leave Britain to find a new start. He might travel to other wizarding communities in Europe, like in France. There, he could discover new magical creatures and spells that are not well - known in Britain. He may also meet other witches and wizards who have different views on magic compared to his British counterparts, which could lead to his personal growth and a change in his understanding of the wizarding world.
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.
He could meet new witches and wizards from different cultures. For example, he might run into a powerful African wizard who has unique magical abilities related to nature magic. Or he could meet a Japanese witch who specializes in charm - making that is based on ancient Shinto beliefs.
Hermione could accompany him. She's always been by his side and would likely follow him out of loyalty and a thirst for new knowledge. Together, they could explore new magical theories in different parts of the world. Another possibility is Hagrid. He has a soft spot for Harry and might want to protect him on his journey. He could introduce Harry to different magical creatures in other countries.
He might go to America. The American wizarding world is different from the British one. There are different magical creatures and a different magical culture. Harry could go there to start anew, maybe help out at Ilvermorny or explore the magical wilderness of the States.
There's a chance he meets a group of nomadic magic - users. These are people who travel across the universe in search of new sources of magic. They could introduce Harry to different forms of magic that are not based on the traditional elements like fire, water, earth, and air that he's used to on Earth. Instead, they might use things like starlight or cosmic energy as a basis for their spells.
He might encounter a hermit who lives in a tree and has some really strange habits. The hermit could offer Naruto some 'wise' advice that is actually just really absurd, like telling him to walk on his hands to find his true path.
There's a chance he meets some magical creatures that can talk in the American wilderness. For example, he might encounter a Sasquatch that has a deep understanding of the ancient magic in America. They could form an unlikely friendship and the Sasquatch could help Harry in his journey to adapt to the new magical environment.
Harry could meet students from Ilvermorny. They would have different personalities and magical abilities compared to Hogwarts students. He might also meet American magical creatures' caretakers who can introduce him to creatures like the Wampus cat or the Horned Serpent. Additionally, he could come across American Aurors who have their own methods of dealing with dark wizards.
Perhaps he leaves to explore the Muggle world. Harry has always had an interest in Muggles. After the war, he realizes he wants to experience life without magic for a while. He could go to university in a big city like London, study a Muggle subject like history or literature. He'd make new Muggle friends and try to fit in, all while still having his magical abilities hidden, which would add an interesting dynamic to his new life.