Adventure is a very common theme. Given her character's history of traveling with the Doctor and having her own adventures, many fanfictions continue this trend, taking her on new and exciting missions. Another common theme is friendship, especially her relationships with the Doctor, her companions, and the friends she makes in her own series. It often explores the deep bonds she forms.
Social media platforms can also be a source. Look for Doctor Who or Sarah Jane Smith fan groups on Facebook or Twitter. Some fans might post links to their fanfiction there or discuss where to find the best ones.
I'm not entirely sure specifically what the 'gorgon city story' is about as it could be a very specific or even a made - up story. It might be related to a place named Gorgon City in some fictional context, or perhaps it's a story with a character or event that has the name 'Gorgon' in it.
In the story of Macbeth, the old gorgon was believed to be the manifestation of evil and fate. The witches' prophecies and their mysterious presence drove Macbeth to his downfall.
In the 'gorgon city story', the main characters could be a diverse group. There might be a young journalist who is trying to uncover the truth about the city. There could also be an old wise man who knows the ancient secrets of Gorgon City and guides the younger characters. And there may be a group of rebels who are fighting against an unjust regime in the city.
Power struggles are likely a common theme. Given it's a 'war' in the title, there would probably be stories about different factions vying for control in the world of Gorgon. Another could be heroism, with characters rising up to face challenges during the war.
One idea could be that Harry's gorgon abilities lead to him accidentally turning some of his friends to stone during a Quidditch match. Maybe his hair gets out of control and the glare from the sun causes the transformation.
Hermione could be a main character. She might be the one who helps Harry understand and control his gorgon powers. For example, she could research in the library to find ancient spells or potions that can suppress the gorgon - like effects when they are unwanted.