One of the recommended attractions near the hotel is Jeonghangpokpo (정방폭포, 正房瀑布). This was designated as a natural heritage of Korea in 2008. Legend has it that the messenger of Qin Shi Huang, named Seobul (徐市), came to Jeju to find the herb of eternal youth. While passing through this area, Seobul carved the characters '徐市過此' onto the cliffs. This act is said to be the origin of the name 'Seogwipo'. (However, in reality, you may not be able to find the characters.)
If you are interested in Jeonghangpokpo, you can walk from the hotel for about 20 minutes by taking the Olle Trail (Course No. 6).
You can find more information on attractions near the hotel at the link below.