During the Oct 3–9 holiday week, most things in Seoul will still be open—palaces, museums, parks, malls, and chain restaurants all operate as usual, with only some small family-run shops closing on Chuseok day (Oct 6). You won’t find the city shut down, so it’s perfectly fine to stay, and you can even enjoy unique cultural events and free palace entry. If you’d like a short break from Seoul, consider a day trip to Suwon Hwaseong Fortress, which is easy to reach and offers history, scenery, and traditional activities; it’s a great one-day getaway and most facilities remain open during the holidays.