Maybe he'll encounter a young genius student who becomes his sidekick for the time he's at school. This student could help him with his high - tech gadgets or offer unique insights into the school's problems. Also, he might run into the principal who is initially suspicious of him but later realizes his good intentions.
Batman could meet Starfire. She has unique powers and a different perspective from Batman. They might have a conversation about her powers and how she can use them more effectively. Also, Batman might be curious about her alien origin and what it means for the Titans' capabilities.
He might start by observing. Aang is a curious person, so he'd likely watch how people live, how they interact with technology. He may also try to find other benders to learn about any new developments in bending. And he'd probably use his kind heart to make friends easily in this new future environment.
It could be that Batman breaks one of his own moral codes in a desperate situation. For example, he might accidentally cause the death of a criminal while trying to stop a major crime. This action, which goes against his no - killing rule, makes the public and the law turn against him, sending him to jail. In jail, he has to face his own inner demons and also deal with the threats from other inmates who see him as a big target.
The Joker could be the main antagonist. Even though Batman is in jail, the Joker could find a way to continue his chaos - making. He might try to get into the prison to torment Batman or use the situation to his advantage by causing mayhem in Gotham City without Batman there to stop him.
Well, he could be there to offer his expertise. Maybe he wants to train the Titans in new combat techniques. He might also be there to check on a potential threat that the Titans are facing and offer his help in dealing with it.
One possible storyline could be that Batman is exposed to a mind - controlling substance. This makes him turn against his allies in Gotham. He might start using his advanced technology and combat skills to take over the criminal underworld instead of fighting it.
In this fanfiction, Harry might see a world where magic has evolved in ways he couldn't imagine. Maybe there are new spells and potions that are far more advanced. He could also encounter the future versions of his friends and enemies. For example, he might find out that Ron has become a very important figure in the wizarding world, or that Voldemort's influence still lingers in some unexpected ways.