One common theme is friendship. Given that they are both strong female characters from different fictional universes in a fanfiction context, their friendship can be explored in various ways, like helping each other through difficult times.
Well, another place to look could be Tumblr. Sometimes fans post links to their fanfictions or even short fanfiction snippets there. You could also join relevant fan groups on Facebook or Reddit. In those groups, fellow fans might be able to recommend some great Hermione Lodge and Cheryl Blossom fanfictions.
In Cheryl Blossom OC fanfiction, a frequently seen theme is the power dynamics. Cheryl comes from a wealthy and influential family in Riverdale, and when an OC enters her world, it creates an interesting shift in the power balance. Sometimes the OC is from a different social class, and how they navigate this difference with Cheryl is a big part of the story. Another common theme is family. The OC might have a different family situation compared to Cheryl, and how their families interact or how the OC affects Cheryl's relationship with her own family can be a central part of the fic. There's also the theme of mystery. Some fics make the OC have a mysterious past or purpose in Riverdale, and Cheryl gets drawn into solving that mystery.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of fanfictions from various fandoms, including Riverdale where Cheryl Blossom is from. Just search for 'Cheryl Blossom' in the search bar.
One great Cheryl Blossom fanfiction could be one where she overcomes her family's dark secrets and finds true friendship. It might focus on her growth from a somewhat villainous character to a more complex and sympathetic one.