If you are in Seoul and don’t understand Korean, I recommend City Light for church.
Seoul has a huge complicated subway system. You can save 100원 per trip if you buy a card that you can add money to when it gets low. And you can also use it on the buses. If you use the card within thirty minutes of getting off the subway, the bus is free.
If you like walking, there is a really long park where a railroad called the Gyeongui Line used to be. The north end of it is called the Gyeongui Line Book Street. Some of it is still being built but most of it is very nice. No motorized vehicles; about two kilometers long.
Close to Anguk station, there is a park/museum for Korean history and culture which is nice. Part of it is free, including tours in various languages. And people like to rent old-fashioned traditional Korean clothes to walk around the area. Also nearby is a park with other palaces/museums that I did not visit.
There is a “missionary cemetery” close to the river at hapjeong-dong with an info center about the missionaries. Next to it is an area bought by the Roman Catholics as a memorial to over a hundred priests who were executed there in the mid-1800s for “introducing western ways.”
In Gangnam (remember “Gangnam-style”?) there is a park containing the tombs of two kings and one queen plus a small historical exhibit and at least a kilometer of walking paths.
There are quite a few hiking routes also, but I didn’t actually get on any. We had a pilgrim on Camino de Santiago recently who had walked from Busan to Seoul. I don’t know the distance, but train takes 2-3 hours.
Google Maps cannot give you directions in Korea for walking, biking, or driving—only transit. For the other modes you need Naver or a GPS device or an OSM app or a paper map.
I enjoyed my month in Korea—but I didn’t learn much Korean!