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.
In the fanfic, it might lead to a tense confrontation. Harry could feel anger towards the Malfoys as they are known for their prejudice. Draco might taunt Harry as usual, and Lucius Malfoy could look down on Harry with his typical haughty attitude.
Harry is strolling through Diagon Alley, looking for new robes. He bumps into Daphne near Madam Malkin's. Daphne gives him a cold look at first, but Harry smiles sheepishly. Then Daphne's expression softens a bit as she realizes it's Harry Potter. They start chatting about how difficult it is to find robes that fit just right, and Daphne mentions a little - known shop where she gets her best - fitting robes.
Perhaps they exchange books right away. Harry shows Daphne his spell - books, and Daphne offers him one of her advanced potions books. This simple act of sharing could spark a connection between them. They might then sit together for the rest of the train ride, chatting about the upcoming school year and speculating on what new adventures and challenges await them at Hogwarts.
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.
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 have to deal with a lot of administrative work. Running Diagon Alley means taking care of all the shops, making sure the wizards and witches who work there are happy, and dealing with any disputes. For example, if two shop owners have an argument over a piece of land in Diagon Alley, Harry would have to step in and sort it out.
Well, in some fanfictions, it could be due to a powerful spell gone wrong that transfers the ownership to him. Maybe a spell meant to protect Diagon Alley's property rights backfires and suddenly Harry is the owner.
In the fanfic, it's possible that they are both there on a secret errand. Harry could be looking for a hidden magical item that he believes is stored in Gringotts for safe - keeping. Daphne might be there under orders from her family. When they meet, they might initially be guarded about their true purposes. However, as they interact, they start to trust each other and decide to collaborate, which could set off a whole new chain of events in the story.
Maybe it's a new character created by the fanfiction author. This new character could have special abilities or a unique backstory that ties into the reason for escorting Harry to Diagon Alley.