I just returned from a two week trip to Korea. I found that eating gluten free was no problem in Korea. I was a bit worried because I only found people complaining online about how difficult it is to find gluten free food in Korea. I had a different experience probably because I was always with a relative who could tell me what is in the various foods. Much of Korean cuisine is rice based and is naturally gluten free. I just avoided the items known to have soy sauce and go choo jang (a spicy paste made of ground red pepper - this usually has wheat). I found if you ask "Does this food have wheat?" people will swear it has no wheat. They don't realize that wheat is contained in soy sauce and items like go choo jang. So it is better to ask, "Does this have wheat or soy sauce or go choo jang?"
More specifics on what I ate:
* As a rough rule, the soups ending in the word "tang" I could eat. Specific examples include gom tang (oxtail soup), sul long tang (like oxtail soup but has strips of beef), gal bi tang (like oxtail soup but made with beef rib), gam ja tang (spicy soup made of potatoes and pork spine), sam gae tang (soup made with chicken that is stuffed with gin seng, rice, and other goodies, it's quite good)
Gom tang and its variants are basically beef boiled forever. I usually ask for the soup with NO noodles just to be on the extra safe side but usually the noodles that are added to sul long tang is dang myun, which is a clear noodle made with sweet potato starch (so should be ok for celiacs).
* Kim bop: this is the Korean version of the Japanese sushi. These are among the cheapest foods you can purchase and there are places everywhere that will make it fresh. I usually got the most plain kind of kim bop, and I avoided the items I knew had soy sauce. I usually poke out the sausage but once I was brave and I ate the sausage and felt ok.
* Kim chee: I was able to eat all kinds of kim chee without problems. One warning: there are some vegetables that are seasoned with go choo jang, which contains wheat, but might look a bit like kim chee. So if you are not sure be sure to ask is this kim chee.
* I was able to eat nang myun, which is a cold buckwheat noodle dish but because my relative made sure that the noodles were totally wheat free.
* I had wonderful pork and duck, simply grilled without any marinades. These sorts of restaurants are everywhere too. Some of my best meals were at these types of restaurants.
* Bi bim bap: I believe other people in this forum mentioned this dish before. Basically rice with various vegetables and egg. Be sure to ask for NO go choo jang because otherwise they might put the go choo jang right in the rice bowl instead of giving it to you on the side.
* There are sweets made of rice flour and somtimes filled with sweet bean paste or sweet sesame paste. They are usually small, round, and I believe called ttuck (don't know how it is romanized).
I hope this is helpful for some people.