1. Visit the local amusement parks! Everland and Lotte World always have discounts, especially for foreigners, during Chuseok vacation. This year, Everland, an amusement park with rollercoasters and a zoo, located a little ways outside the city, is offering a reduced admission of only 27,000 won http://www.everland.com/web/multi/english/everland/everland_guide/news/1215349_10988.html
2. Use this time to explore all of Seoul's great palaces! Most people go to Gyeongbokgung, but few ever visit Deoksugung, Changdeokgung, and Changgyeonggung. Changdeokgung is probably my favorite of all the palaces, and Changgyeonggung has a "secret garden" that you can take a tour of. All of the palaces as well as Jongmyo shrine and the Namsangol hanok village have cultural performances and activities during Chuseok as well.
3. Go Hiking. Fall is upon us, and the temperatures are starting to drop. With Seoul being so much emptier now than it normally is, its a great time to take advantage of it and head to the mountains. There's mountains all around Seoul, but a few great places to go is Bukhansan national park in the north or Gwanaksan in the south.
4. Museums. Seoul has some great, free museums. Some will be closed, but the National Folk Museum, the National Museum of Korea, the Korean War Memorial in Yongsan, and the Seoul Museum of History remain open through the long weekend. If you haven't checked it out yet, the War Memorial (at Samgakji) is my personal favorite. It's huge and can easily take several hours to see it all.
5. The Han River: Now is the time to rent some bikes, rent some kayaks (at Ttukseom resort station), and enjoy the much quieter than normal Han river. The weather is looking to be great this weekend as well.
6. Take a day trip to Hwaseong Fortress in Suwon. This year there's free admission on the day of Chuseok. Hwaseong is a beautiful fortress and worth a day trip if you haven't been there yet. It takes about 1 hour by subway from the middle of Seoul. http://english.visitkorea.or.kr/enu/ATR/SI_EN_3_1_1_1.jsp?cid=264204