Not sure what grades you are teaching but if their level is high enough you could do something about rules or laws.
What I have done before is I showed them basic sentence structures using MUST and CAN/CANNOT and talked about laws in different countries. Like driving age, mandatory military service, etc. Just things that vary from country to country. You can ask the Korean students and Japanese students about laws in their countries and compare them.
Then, prepare a list of questions and make groups of 4 students. (have some Korean and some Japanese students in each group). Ask them to make a new country. What is the name of the country? Which language will it speak? What will the driving age be? Will military service be mandatory? What will the flag look like?
I have done this with high school before and it worked good. At the end, I had the groups give a presentation about their country. Some of the Ss had very funny or creative answers. (National language: body language)
If your students level is not that high, just get them into small groups and have them work together with students from the other country. This will force them to use English to communicate and be a good cultural experience for them. You could talk about food from their countries and make a restaurant menu, listing prices in Korean Won, Japanese Yen, and US Dollar. Talk about how much a McDonalds hamburger or a bottle of water costs in different countries.