Well, the kid might go on a journey to discover a new spell that was lost in time. Just like Hermione was always into books and knowledge, her kid could be on a quest to find ancient magical texts hidden in a secret library in Hogwarts.
She would no doubt instill strong moral values in her child. Given her own experiences fighting against evil, she'd teach the kid to always stand up for what's right and to be kind to all magical beings. She might also teach the kid self - defense spells early on to protect themselves. For example, the Shield Charm and the Stunning Spell. And she'd make sure the kid understood when it was appropriate to use them. Also, Hermione would likely involve the kid in her research projects, sharing her passion for magical discovery with the next generation.
One possible plot could be that Hermione's kid inherits her love for knowledge. Maybe the story shows the kid starting at Hogwarts and struggling to live up to the expectations of being Hermione Granger's child. They could face pressure from peers and teachers alike, but ultimately find their own path in the magical world, perhaps by specializing in a new area of magic that Hermione hadn't explored much.
It could be Ron Weasley. In many post - war fanfictions, Ron and Hermione get married and have children. Ron would be a great father, teaching the kid about wizarding traditions and Quidditch, while Hermione focuses on academics.
One possibility is that the kid has to deal with the prejudices from both the Gryffindor and Slytherin sides. Since Hermione is a Gryffindor and Draco is a Slytherin, their child might be caught in the middle of the long - standing rivalries between the two houses.
Survival is a common theme. Hermione has to use her intelligence and resourcefulness to stay alive on the streets. Another theme is secrecy, especially about her magical abilities which could draw unwanted attention.
One great fanfiction idea could be that Draco and Hermione are forced to swim together as part of a magical school competition. Maybe they start off as rivals, but as they swim through enchanted waters filled with magical creatures, they begin to see each other in a new light and develop an unexpected friendship.
One great truth or dare fanfiction could involve Hermione daring Harry to use a spell he's never tried before in a non - dangerous situation. This would lead to some comical attempts and a deeper understanding of the magic they have yet to fully explore.
Maybe they embark on a journey to rescue a captured wizard or witch. They use their different strengths - Hermione's strategic thinking and her brother's charm or ability to make quick friends in the wizarding world - to plan and execute the rescue mission.
One could be the Thestral. Since Hermione is very intelligent and curious, her discovery and study of Thestrals, which are invisible to those who haven't witnessed death, could be an interesting plot. Another could be the Niffler. Hermione might have an adventure trying to keep a Niffler from stealing shiny things in a museum or a wizard's home. And the Phoenix is also a great choice. Hermione could be involved in a story where she helps a Phoenix that is in trouble, perhaps injured or lost, given her kind-hearted nature.
Perhaps they embark on a journey to find a lost magical creature. Hermione would be excited to study the creature, and Sirius would be there to protect them during the search. Along the way, they might encounter other interesting characters or face challenges that test their friendship and abilities.