One possible plotline could be Harry and Hermione exploring the hidden secrets of Godric's Hollow. Maybe they discover an ancient magic there that was left by Godric Gryffindor himself. Another could be them facing some dark forces that are also interested in the secrets of the place.
In certain 'Harry and Hermione Godric's Hollow fanfiction', a great plotline could be that they are on a quest to protect Godric's Hollow from an impending threat. They could be trying to find a powerful magical artifact hidden there to use against the dark forces. Along the way, they might have to deal with various challenges like magical traps, and also strengthen their bond as friends or even develop a romantic relationship, depending on the nature of the fanfiction.
Often, it could be Death Eaters or their remnants. They might be after the same secrets or power sources in Godric's Hollow as Harry and Hermione.
Well, a possible plotline is that Harry starts to have dreams or visions related to Gryffindor's past. These could guide him in his fight against Voldemort. For example, he could see how Gryffindor defeated dark wizards in his time and use that knowledge. Also, Harry might face challenges within Gryffindor house itself. Some students could be jealous of his new status, while others might expect him to lead them in a more direct way.
Some fanfictions explore a different relationship dynamic between them. Maybe Harry has a problem that only Hermione can understand and help him with, and this brings them closer in a way that's different from their normal friendship. It could be something related to his connection with Voldemort or his family history.
One interesting plotline could be where Fairy Godric uses his magic to protect Sookie from various supernatural threats in Bon Temps. Maybe he creates a magical shield around her home.
One interesting plotline could be Harry and Hermione discovering a long - lost secret vault in Gringotts. Maybe it contains powerful magical artifacts that can change the course of the wizarding war. Another could be that they are on a mission to retrieve something from the vault that is crucial for their fight against Voldemort, like a spellbook with ancient and powerful spells.
Perhaps a plot where they all become animagi and have to use their animal forms to solve a mystery in the Forbidden Forest. Draco as a sleek snake, Harry as a stag, and Hermione as an otter, they must navigate the forest's dangers and uncover the truth about a strange magical disturbance.
One possible plotline could be that they are practicing magic for an upcoming difficult exam at Hogwarts. They might be working on advanced spells like the Patronus charm and Hermione is helping Harry perfect it.
One possible plotline could be that they escape from a dark wizard's lair. Maybe they use their combined magic skills and Hermione's extensive knowledge to find a secret passage out. Another could be escaping from a dangerous magical creature's territory by using clever spells and potions.
One possible plotline could be Hermione using her intelligence to create a stable and loving home environment for Harry. Maybe she helps him deal with his PTSD from his past traumas. Another could be them facing magical threats together as a family, with Hermione teaching Harry new spells and ways to protect himself.
In some fanfictions, their training might involve time - traveling. Maybe they go back in time to learn from the founders of Hogwarts. Harry could learn how to better control his connection to Voldemort through this time - traveling training, and Hermione could study ancient magic from the founders. This would add a whole new dimension to their skills and knowledge.