I'm far from an expert, but I've lived in Korea for almost five years and I've observed a lot in that time/heard a lot from Korean friends and co-workers. There is a tendency for Koreans to look down on Southeast Asians. Much like how many conservatives from the US view immigrants from South and Central American countries, Koreans see Southeast Asian immigrants as people who come to Korea to "steal jobs" (which is, of course, ridiculous). Also, because of their darker skin tone, there are Koreans who view Southeast Asians as uglier and mentally inferior to Koreans. If you watch Korean sketch comedy programs, you'll often see the comedians pretending to be and mocking SE Asians, especially Thai. There also a lot of Korean men who seem to treat SE Asia as their playground. A year or two ago, there was an expose on Korean men who go the Philippines, hook up with and impregnate women there, promising to bring the women to Korea, and then returning to Korea alone, abandoning their children and the children's mothers. Look up the term "Kopino" if you're interested in reading more. There's also growing animosity to the Chinese. A couple of years ago, there was a horrific murder that was committed by an ethnically Korean Chinese (called Joseon-jok) immigrant, and it sparked a lot of discrimination against Joseon-jok immigrants. Recently, a lot of wealthy Chinese entrepreneurs started buying large patches of land on Jeju-do, thus driving up the prices on the island, so there's a lot of grumbling among Koreans and protests asking the government to curb the sale of land to Chinese buyers. Among my Korean friends, there're a lot of complaints about Chinese tourists being loud and rude, but even my Chinese friends here agree that tourists can be that way, haha~ The most complicated relationship is with Japan. Liberation from Japanese occupation is still a relatively recent event, so there can still be a lot of nationalistic animosity against Japan, especially among the older generation that still remembers the occupation. Most Koreans seem to hate the current prime minister of Japan, and there's a high competitive nature Korea seems to have against Japan. But, out of the other Asian countries, Korea seems to respect Japan the most? It's a weird dynamic, haha~
But, yeah, it's important to remember that Korea is a very insular, ethnically homogeneous country that only very recently has experienced a boom in multiculturalism. There are a lot of Koreans among the younger generation that embrace the increase of immigrants in Korea, but there's also a large segment of the population that feels even more the need to bunker down and protect the "pure" Korean identity. The Korean government is putting effort into promoting diversity and in creating programs to help immigrants learn the language and adjust to the country (I took one such course in order to get my residency visa). But, like I said, this is all based on my own observations as someone who is basically a Western immigrant living in Korea, so this is all very general!