They might decorate their home with lots of Pokémon - themed items. There could be Pokémon plushies on the couch, Pokémon posters on the walls. Ash would probably have his trophies and badges on display in a special corner. Serena would add some nice floral arrangements to give it a homely feel.
They could have all kinds of adventures. Maybe they discover a rare Pokémon in a hidden forest. They might also meet some interesting characters along the way who teach them new battle strategies or share old Pokémon legends.
They might live in a cozy cottage near a Pokémon forest. Ash could go out every day to train and catch new Pokémon while Serena takes care of their home. She could also start a small garden with Pokémon - friendly plants. At night, they'd share stories about their day over a warm meal cooked by Serena.
One possibility is that they could explore the beautiful Kalos region together. They might visit all the different gyms that Ash didn't get to fully experience before. Serena could also introduce Ash to more of the local cuisine and they could have picnics in the scenic areas of Kalos. Maybe they'd even participate in some local festivals and make new friends together.
One idea could be that they embark on a new adventure in a region neither has visited before. They face unique Pokémon and challenges together, which strengthens their bond. For example, they might come across a rare Pokémon that is said to only appear to those with a strong connection. As they work to catch it, they realize their feelings for each other have deepened.
In Kanto, they might meet some trainers who mistake Serena as Ash's girlfriend. At first, it could be embarrassing for them, but as time passes, they might start to see each other in a new light. They'll have more time to talk, share their dreams, and support each other. Ash could help Serena become a better Pokémon coordinator in Kanto, and Serena could help Ash with his Pokémon training strategies. This mutual support will strengthen their bond.