Just finished an amazing cycle tour from Seoul to Busan, South Korea on the Four Rivers Route trail. We exclusively camped, and couchsurfed across our 12 days cycle. This kept costs down to €40 for our entire 18 day trip in South Korea. People were pretty accepting of wild camping and we didn't have any issues.
The trails are so beautiful, and consist of cycle ways and paved road the entire journey. It was exceptionally hot and humid (August) so if you are doing the trail with kids I'd recommend a more temperate month.
I'd love to do this trip again when I have kids 🥰
by Obvious-Cookie444