The town's doctor is another character that is popular in 'hometown cha cha cha fanfic'. His kind and helpful nature makes him a great addition to many storylines. He could be involved in a medical emergency in the town that brings all the characters together. Or he could have his own love story within the context of the fanfic, perhaps with a new character or one of the existing ones in a different way.
I think the grandma character is also quite popular. She has a lot of wisdom and her own unique charm. Fanfics might feature her giving advice to the younger characters in different situations, or even having her own little adventure in the town. Also, the group of local fishermen friends are often included. Their banter and loyalty to each other make for great fanfic material.
The two main characters, Hyejin and Du - shik, are very popular to feature. Their relationship in the show was so endearing that fans love to explore more of their story in fanfics. They could be put in different scenarios, like going on a trip together outside the hometown or dealing with a family crisis together.