Thanks so much for the recommendation, @Brotherjeep! Chiaksan National Park looks beautiful, and I appreciate the tips about the Guryong Campsite. Shared shower facilities do take some getting used to, but I'm sure it will be a unique experience. I also came across these tourism statistics for Seoul—informative on weather, transport, culture, etc.
https://gowithguide.com/blog/tourism-in-seoul-statistics-2023-the-ultimate-guide-5535. It really helped give me a well-rounded picture of what to expect in South Korea. Guryong seems perfect for hiking the park.