I might have some experience in this area. I had a Korean boy live with us for 5 years. In fact, we were his legal guardians. In our area, there are a lot of Korean students, so our foster son had a large Korean community to interact with, especially through Korean church congregations. He usually spent most of his winter school break on a retreat with his Korean church. He went home every summer to visit his parents, and he is now a student at Rutgers Univ.
This might sound a little strange, but I can tell you that one thing our foster son told us, and his friends told us as well, is that blatantly American items are not received well. For instance, I made a mistake once of giving him a Christmas ornament that had Santa dressed in red, white and blue and holding an American flag. The Korean boys told me that those were things that they'd be teased about if they displayed in Korea. I was offended at first, but I got over it. (Later I had a whole world of things to be offended about in our situation, but that's a long, off-topic story.) Our foster son's sister lives with a family in our area, as well. I tutor her. She was born here and so is an American citizen, but she lived in Korea from the age of 8 until 15. Emotionally and culturally she is Korean. Even though she travels back to Korea on an American passport, she plays down her American citizenship there. As Americans, we may bristle at the idea of someone not really enjoying our patriotic things, but that's their way.
With our foster son, and in fact with our own sons when they were teens, gift cards were always the best thing. Straight up cash is another good gift. In Korea, cash is an appropriate gift on a lot of occasions. Our foster son received quite a bit of cash from his relatives when he visited Korea, and church members also gave him cash for Christmas and birthdays. In fact, for Christmas, I will giving our foster son's sister cash wrapped in an interesting bookmark.
Is your sister's exchange student staying in the U.S. after this year? There is a very big push in Korea to have children come to school here and then go on to American colleges (as well as other Native English speaking countries). Koreans don't think of "exchange" the same way we do. We think of it as a one-year experience. It's very much a long-term idea for them. So even though this particular student may stay only one year in your sister's home, he may move to another host family next year. In which case, this young man will be traveling and moving a lot and won't be able to take any sort of large items with him. Think portable or consumable.