There are numerous valleys in Chiak national park.
If you want to enjoy camping in the valley, you have to make a reservation in advance especially in the vacance season. Sadly, most websites offer their services in Korean only.
(official website from Korean national park service)
(the place i recommend)
Meanwhile, there are also some valleys not widely known but enjoyable without making a reservation. Photos are taken around Sinlim forest.
There’s a cafe named ‘Red roof’ located in 262 Seongnam-ro, Sinlim-myeon, Weonju, Gangwon-do. She will give every information you need. If you bring some meat to BBQ, you can use the facilities with 20,000 won. Please enjoy your summer!