Maybe Neville. He has grown a lot in his magical abilities and his courage. He could bring his knowledge of herbology, which might be useful in different parts of the world. Luna Lovegood could also be a great companion. Her unique perspective on magic would help Harry see things in a different light during his travels.
Harry Potter might visit ancient magical sites around the world. In Egypt, he could explore the pyramids which are filled with ancient spells and hidden chambers. He may also learn about different forms of magic practiced by local wizards in various countries.
He might meet versions of himself from different timelines or parallel universes. Also, there could be new and unique magical beings that the author creates just for the fanfiction. For example, a race of half - human, half - phoenix creatures.
In such fanfictions, one interesting scenario could be Harry Potter visiting the Great Wall of China. He might use his magic to explore the hidden parts of the wall that are not accessible to Muggles. Another could be his visit to the Amazon rainforest, where he discovers magical creatures unique to that area and has to use his skills to protect them from dark wizards who want to exploit their magic.
In certain 'Harry Potter travels to other world fanfiction', Harry could end up in a world where magic is used in a more primitive way. He may find that the wizards there use potions made from rare plants that don't exist in his world. And he has to use his skills to figure out how to communicate with these wizards, as their language of magic is different. He might also discover new forms of magical transportation, like floating stones that can carry people across great distances.
He could meet his future children, if he has any. They would likely be powerful wizards or witches with their own adventures. Also, he might run into the future versions of Hermione and Ron. They would probably be in important positions in the wizarding world, like Hermione might be a headmistress at Hogwarts or something.
Common characters he could meet include an au Ginny who is a powerful seer. There might be a Hagrid who is a tiny, timid man instead of the large, boisterous one we know. He could also encounter an au Sirius Black who is a Death Eater, which would be a shocking twist. Additionally, he may run into an au Professor McGonagall who is more of an artist than a Transfiguration teacher.
Well, in such fanfiction, Harry Potter could meet different versions of Dumbledore. In one universe, Dumbledore could be a dark wizard instead of the wise mentor we know. He may also come across alternate versions of Sirius Black. Maybe in some universes, Sirius is still in Azkaban for a crime he actually committed. Additionally, he could meet different versions of Luna Lovegood, some of whom might have no interest in the strange and wonderful things she loves in the original universe.
There were many doujinshi novels where Harry Potter transmigrated to other worlds, such as:
1 Harry Potter and the Sorcerer's Stone to Draco and Malfoy
2 Harry Potter and the Chamber of Secrets to Hermione and Ron
3. Harry Potter and the Prisoner of Azkaban to Rise of the Dark Mage
Harry Potter and the Goblet of Fire to Rise of the Dark Lord
Harry Potter and the Order of the Phoenix Transmigrated to the World of Voldemort's Return
These novels all had the plot of Harry Potter traveling to another world.