They could go on a mission to find a lost pet in the village. Since they are the same age, they would have similar levels of energy and curiosity. Naruto's determination and Hana's skills with animals might combine well to track down the pet and return it to its owner.
Well, they might get into all sorts of trouble in the ninja academy. Maybe they'd compete in a friendly way during the academy's training exercises. Naruto would be showing off his new jutsu attempts, and Hana could be demonstrating her knowledge of animal handling. And together, they could form a team for a special academy project, like exploring an old part of the village that's said to be haunted by ninja spirits. They'd face their fears together and learn more about the history of the village.
One possible adventure could be that they are both chosen to participate in a village - wide scavenger hunt. Naruto would be excited for the challenge and the chance to prove himself. Hana, with her connection to animals, might get some help from the village's stray dogs to find the items on the list. Along the way, they could encounter other teams trying to outwit them, and they'd have to use their wits and skills. Naruto could use his shadow clone jutsu to cover more ground, while Hana uses her knowledge of the village's nooks and crannies to find hidden items.
They could go on a mission together to retrieve a lost ninja art scroll. Since they are the same age, they might have a competitive yet friendly relationship during the mission, constantly trying to outdo each other in combat skills but also having each other's backs.
They could go on adventures to discover ancient ninja secrets. Since they are the same age, they might team up to explore hidden places that are said to hold great power or knowledge. Maybe they would search for lost jutsu together and face various challenges along the way.
Well, they might embark on a journey to find a rare herb that has the power to heal any injury. Shizune's medical knowledge would be crucial in identifying the herb, and Naruto's strength and determination would keep them safe from any threats along the way. They could also get into all sorts of scrapes with other ninja clans who also want the herb for their own purposes.
Naruto and Minato could have adventures in the spirit world together if they were the same age in fanfiction. They could face powerful spirits and learn spiritual ninja techniques. Their combined courage and determination would help them overcome the challenges there. They might also meet the previous Hokages in the spirit world and get some unique training or advice, which would be very beneficial for their growth as ninjas.
They could have training adventures together. Since they are the same age, they might compete in various ninja skills, like who can master a new jutsu faster. Maybe they'd go on missions side by side, facing challenges and relying on each other's unique abilities.
Well, they could embark on a journey to find other tailed beasts and try to form a new kind of bond among them. This would be an adventure full of challenges as some of the tailed beasts might be hostile at first. Naruto and Kyuubi, as brothers, would use their combined strength and Naruto's persuasion skills to make peace with them. Along the way, they would also learn more about each other's capabilities and grow closer as brothers.
Another plot could revolve around their family backgrounds. Naruto being an orphan and Hana having a family in the Inuzuka clan. Hana might introduce Naruto to the Inuzuka way of life, like how they bond with their ninja dogs. This could give Naruto a sense of family he has always longed for. And together, they could face the prejudice some have towards Naruto because of the Nine - Tails within him, with Hana standing up for him.
They could go on an adventure to find a powerful treasure that combines the power of the One Piece and some kind of ninja - related artifact. Maybe they'd have to fight against a new enemy that is a combination of pirates and rogue ninjas. They might travel to new islands where Naruto's ninjutsu would be useful for exploring hidden caves, and Luffy's stretching ability would help them reach high places or cross large gaps.
They could have some really cool adventures. For example, they could team up to take on a powerful villain that is causing chaos in both their worlds. Naruto's ninja skills combined with Batman's detective skills and gadgets would make for an unbeatable team. They might also go on a journey to find a way to send Naruto back to his own world if that was the case, encountering all sorts of strange creatures and obstacles along the way.
They could go on a mission to save the village. Naruto's experience, Inojin's skills and Himawari's hidden potential could combine to defeat a powerful enemy threatening the Hidden Leaf. For example, they might face a rogue ninja who has a new and dangerous jutsu. Naruto would lead the way with his Rasengan, Inojin would use his art techniques to create distractions, and Himawari could use her Byakugan to spot the enemy's weak points.