Hiking is perhaps the number one thing to do in Seoul. Literally, the entire country is made out of hills and mountains. If you walk around any university campus in Seoul, you will be forced to climb up a steep hill in order to reach your classes, dorms, or restaurants.
It is a struggle at times. For example, there are famous mountains like Bukhansan, Dobongsan, Hallasan (in Jeju), Achasan, Namsan, and so many more tall mountains. Oftentimes, you will find older South Koreans decked out in hiking gear because they center around these mountains to hike. Perhaps, this is why they have so much stamina and are so healthy because they work out frequently by walking out their door. You will work up a sweat trying to walk around.
At the bottom of the mountains of the entrances or exits, there will be many restaurants and places to rest and recover from the exercise. There is also always a convenience store where you can buy stuff. At the end of your hike, you can also clean your shoes and pants with an air blower that blows air for free. When you go hiking, there is always exercise equipment on the way to the top where you can watch people exercise. These are also for free and very clean to use.
Another thing to do is visit Namsangol Hanok Village sits at the bottom of Namsan. It is a famous playground for the summer in Seoul where children would play traditional games like ddakji and more! There is a pavilion built named Cheonugak where clean water flows and this was believed to bestow upon people supernatural powers. The current day Namsangol Village consists of 5 commoner houses and 5 houses of the most powerful Confucian bureaucrats. They were moved to this area along with pieces of furniture to illustrate and educate today’s people about the life of their ancestors.
It is a fun place to visit, especially with kids. But there are other things to do in the surrounding area after you visit the playground. You can walk up towards Namsan Tower and perhaps ride the cable car up! It is a beautiful sight, particularly at night, so make sure to visit after sunset.
Sidenote: A good tip to keep in mind when going to the bathroom in South Korea. Sometimes you might find a squat toilet. Most times, you will find a western toilet. Keep in mind, that the public bathrooms may run out of toilet paper and they are surprisingly clean. Unlike private establishments, the private bathrooms in restaurants and cafes are questionable. I would suggest going to the public bathroom over the private bathroom. In comparison, to the United States, I do not suggest going into public bathrooms or private bathrooms unless it is your own home.