There are lots of great cycling routes around the country (you can get a bike passport and ride the 4 main rivers, east coast, Incheon to Busan (cross country) and around Jeju Island. Actually, most rivers and streams have paths around them and there are lots of farm roads. Bikes can be taken on some trains and on subways on the weekends. They can also be placed under intercity busses. The main Korean navigation apps include bike routes. There are a few private no-kill shelters and animal rights groups that would probably love some attention!