If you ever find yourself especially sleepy in Korea, a jjimjilbang (찜질방) is a good place to go for a few hours. We went to Dragon Hill Spa (드래곤힐스파) the last time we were in Seoul to soak in hot water and slumber on the floor.
On weekends, it’s 14,000₩ for day (5:00 am - 8:00 pm) or night (8:00 pm - 5:00 am). Lots of variety in rooms (e.g. all temperatures, including an ice room and a salt room) and baths (e.g. ginseng and medicinal water).