Another possibility is that he works at the Ministry of Magic. Given his status as the Boy Who Lived, he might be given some special tasks or a regular job in a department. For example, he could be in the Auror department, learning from the Aurors and doing some basic tasks like filing reports or helping with the research on dark wizards.
He could work at Weasleys' Wizard Wheezes. He has a good relationship with the Weasley family, and it would be a fun place for him to work, helping with inventing and selling all kinds of magical pranks and toys.
Maybe he would work at Hogwarts. There are always things to do around the school during summer, like helping with the maintenance of the castle or taking care of the magical creatures in the Forbidden Forest under the guidance of Hagrid. This would give him a chance to be closer to the place he loves and also learn more about Hogwarts.
Hagrid could be a great help. He has a lot of connections in the wizarding world, especially with those related to magical creatures. He might introduce Harry to someone who needs help with taking care of or studying magical beasts, and thus get Harry a job in that area.
Well, he might work at Weasleys' Wizard Wheezes. He could help George and Ron with inventing new products and dealing with customers. It would be full of magical mishaps and lots of fun.
He could meet other young wizards and witches who are also working summer jobs. Maybe some from other wizarding schools.
Well, he could work at Hogwarts during the summer for a change. Maybe he's helping Hagrid with the care of magical creatures. He would get to interact with new and dangerous beasts, and at the same time, he might learn some new spells to keep them in check from other professors.
Obviously Harry would be one of the main characters. And Hermione might also be involved, perhaps she helps Harry get the job or gives him advice on how to do it well.
In a 'Harry Potter Summer Training' fanfiction, perhaps the training is organized by some of the older students who have graduated but still want to help. They could be teaching the younger students advanced dueling techniques. Harry might discover a new aspect of his magic during this training, something that has been dormant until now. For example, he could have an affinity for a type of magic that is rare, like time - related magic. The story could then revolve around him exploring this new power under the guidance of the older students.
Dumbledore could be the instructor. He might have a special training program in mind for the students. He could teach them about the deeper mysteries of magic, like the secrets of the Hallows or the true nature of the Deathly Hallows. His wisdom and experience would make him an excellent teacher for the students during the summer training.
In this fanfic, Harry might get a job as an Auror. He would be involved in solving magical crimes, going on dangerous missions, and working with his old friends to keep the wizarding world safe.
Perhaps it focuses on the changes in Harry's relationships. He might grow closer to some friends while drifting apart from others. For example, his bond with Hermione could strengthen as they explore some new magical mystery together during that summer. And his relationship with the Dursleys could also take a turn, like they finally start to show a bit of understanding towards him.
He could be a martial arts instructor. Goku is a master in combat, and teaching others his skills would be a great job for him. He could train students in the ways of martial arts, sharing his knowledge and experience.