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.