An incredible island with volcanic lava tubes, the beautiful Hallasan National Park, and a distinct culture from that of the mainland. Ilchul-bong is a must see crater located on the eastern edge of the island. This paradise is rich with delicious seafood, friendly people, fascinating "stone grandfather" statues, and the well-document stories and traditions of Haenyeo women divers. Visitors planning a trip should really consider their timing, because for Koreans there are definitely high and low seasons in regards to tourism, and the island can become quite busy. Moreover, foreign visitors can rent cars or smaller vehicles on Jeju, which is less restrictive than mainland South Korea. Setting up your hotel should also be considered carefully, Jeju City or Seogwipo. I chose the later, but it really depends on your travel priorities.
The distinct dialect, culture, and landscapes of Jeju make it feel like an island country. Jeju is particularly rewarding with longer stays walking the olle-gil trails and visiting Hallasan National Park on multiple treks (not just the crater lake).
Hallasan National Park
Keep in mind the crater lake is not the end all be all for this park. If you don't do the summit, you can hike to Saraoreum, walk the boardwalks at the 1100 Altitude Wetland (Ramsar Wetland), or hike the numerous trails within the park.
Ilchul-bong
A more rigorous hike than expected, though still relatively short, you will be rewarded with expansive views of the crater and the island itself. Furthermore, near the coastline, there are WWII remnants related to the Japanese Occupation of Jeju.

Lava Tubes
Having little knowledge at the time, I simply was impressed by the size of the tunnel / chamber. This is not the type of cave where you will see wondrous cave formations typically seen in Karst caverns. Lava rock is particularly rough / sharp, so proper footwear is a must.
Besides the 3 inscribed areas (Hallasan, Geomunoreum Lava Tube System, and Seongsan Ilchulbong), there is talk of expanding the world heritage property. Particularly, Western Jeju's Suwolbong Tuff Cone and Chagwi Coast. I would certainly welcome an extension. Nevertheless, a trip to Jeju is a highlight for many who visit Korea.
Logistics
How do you plan on arriving to Jeju? You can fly directly from Gimpo airport. You can also take ferries from Mokpo, Goheung, and Yeosu (plus a few other locations). These are important considerations related to the rest of your Korea itinerary.
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