He might form closer bonds with local heroes in his neighborhood. Since he's not at UA, he would have more time to interact with the heroes who operate near his home. They could become his mentors or friends, guiding him in his hero journey.
His relationships with his family could be strengthened. Without the demands of UA, he can spend more time at home. This could lead to deeper conversations with his mother and a better understanding of his father's legacy. He might also be more involved in his local community, forming relationships with ordinary people who support his hero dreams in different ways.
Another possibility is that he joins a different hero school. Maybe there's a smaller, more specialized school that focuses on a particular aspect of heroism that UA doesn't. For example, a school that specializes in rescue operations could be a great fit for Izuku's empathetic nature.
It could be his mother. She might think that UA is the best place for Izuku to become a hero and force him to go there for his own good, even if he has some doubts or hesitations.
In this kind of fanfiction, Izuku might face a lot of challenges. Maybe he is forced to go to UA by some external power or person against his will. He could struggle to adapt to the new environment at UA, having to deal with difficult classmates or strict teachers. Also, his own self - doubt might intensify as he didn't choose to be there on his own terms.
His relationship with All Might would be very different. Instead of being a successor, he might become more of a protege in a general sense. All Might could still mentor him, but their bond wouldn't be centered around One for All.
He could form relationships with other outcasts. People who also don't have a home or a place in society. They could band together and form a sort of 'family' of misfits.
In a modern society, Zuko could form romantic relationships too. He would be attracted to someone with a kind heart and strong values. His relationship would start slowly as he's not used to modern dating customs. He would be very protective of his partner. And his partner would have to understand his past and the fact that he's still adjusting to this new world. They would grow together, learning from each other's different backgrounds.
Edward could form strong friendships with the hobbits. Hobbits are known for their loyalty and kindness. They would be curious about Edward and his abilities. Edward, in turn, would appreciate their simple yet warm - hearted nature. He could help them in their adventures, using his alchemy skills, and they could offer him a sense of home and community that he might be missing from his own world.
He would probably form some interesting friendships. He might befriend people who are into martial arts or those with a sense of justice like him. He could also have a mentor - like relationship with some, teaching them about his ninja ways.
Gohan might form a mentor - like relationship with some of the younger Fairy Tail mages. He has a lot of combat experience and could teach them about discipline and the importance of training. He could also be friends with the more powerful mages, like Natsu, and they could spar together to improve their skills.
Tsuna would probably form some interesting relationships. He might be friends with Izuku Midoriya. Both start off as rather timid characters and have to grow into their powers. They could bond over their shared experiences of self - discovery and improvement. Tsuna could also have a friendly rivalry with Bakugo. Bakugo's brash nature might clash with Tsuna's more laid - back (initially) personality, but they could also learn from each other in terms of combat and determination.