If you enjoy nature, hiking one of the olle trails is a must-do while you're in jeju. It will not be an easy hike and not all parts of the trail are scenic but there are sufficient sights to blow you away and be left in awe of nature. This is also the best way to experience jeju's natural beauty (after all this is what its most famous for and not for teddy bears). It is also arguably the least touristy thing to do during your trip here. You can do as long or as short of the trails as you like; there are trails passing through hot tourist destinations where you'll see many tourist buses, local villages, rice fields, even resorts. You'll walk on sand, on rocks by the ocean, and if you time it correctly you'll be able to catch a gorgeous sunset along jeju's coastline. Be sure not to get stuck in a remote area after sunset as it can be difficult to get out. If you're doing a multi-day hike, there are many pensions located along the olle routes and you can just pop in for a night.
Suggest to go with at least one other person in case you get lost (there are some places where the markings are not so visible/well maintained). If you rented a car, dont drive. Wear comfortable shoes and bring lots of water and snacks!More