Perhaps the alley is a place where the teacher believes Harry can learn more about the less - known aspects of the wizarding world. They could visit old, dusty shops filled with strange curiosities. The teacher might introduce Harry to some eccentric witches and wizards who have a wealth of knowledge that isn't taught at Hogwarts. This experience could broaden Harry's understanding of magic and its many forms.
Well, it could be that the teacher suspects some dark magic activities in the alley and takes Harry along to show him how to detect and deal with such things. They might encounter some dodgy characters along the way, like shady potion sellers or wizards trying to sell illegal magical artifacts.
Well, he could meet some new and mysterious characters. Maybe a young wizard with a strange power who becomes his friend or an old wizard with a hidden agenda. He might also discover a new magical shop that sells unique items not found in the regular Diagon Alley stores.
Well, he might encounter a new magical creature that is not in the original books. For example, a tiny dragon that can speak and becomes his little friend, guiding him through the Alley and showing him some hidden shops.
One possibility is that their meeting is not so friendly at first. Daphne, coming from a certain Slytherin - pure - blood mindset, might be a bit haughty towards Harry. But as they talk, Harry's kindness and honesty could break through her initial prejudice. They could end up having a deep conversation about the differences between the houses at Hogwarts, and how they both want to make the most of their time at school, despite their different backgrounds.
He could meet a famous wizard author who is signing books in Diagon Alley. This wizard could give Harry some valuable advice about his future.
He might meet some interesting new friends. In fanfiction, the gay club could be a place full of unique characters. Harry could engage in deep conversations about various topics like art, music or the LGBT+ community's experiences.
He might encounter some strange magical creatures that are only found underground. For example, there could be a new type of goblin or a magical mole with special powers.
He could encounter a new magical creature. The goblins at Gringotts are known to have various magical creatures guarding different vaults. Maybe Harry comes across a rare and friendly creature that helps him on his journey. For example, a small fire - breathing dragon that he befriends and it later aids him in a battle against Voldemort's forces.
Perhaps when Harry goes to Hermione's house, they end up having a deep conversation about their future in the wizarding world. They could discuss their plans for after Hogwarts, like Hermione's dreams of reforming the Ministry of Magic and Harry's thoughts on teaching Defense Against the Dark Arts at Hogwarts. They might also share some personal feelings they've been hiding from each other.
He might meet some strange magical creatures there that are used for experimental treatments.
In some fanfictions, when Harry Potter goes through the mirror, he might find himself in a parallel magical world. This world could have different versions of his friends and enemies, and he may have to face new challenges to find his way back to his own world.