The weather at this time of year in Korea is about as warm as it gets, so if I was in your shoes my primary interest would probably be comfort, as in avoiding anything strenuous out in the heat and humidity, but each to his own.

During much cooler weather-- admittedly, more than a few years ago-- I did the hike from Pyeongchang-Dong to Dae Nam Mun. I thought it was interesting, and the view from the gate is pretty nice, as you can see from the panoramic shot linked at the URL above.

I don't know how it would be now, but I also took a day trip out to Kangwha-Do a couple of times, where I was able to look across the water (northern part of the island) to see North Korea. What was amazing to me was that the Norks had completely denuded all the ground around the coast, apparently to remove anything that might be used to cover movement in or out of North Korea. At the time, I took a bus from Seoul; I would guess the bus probably still runs out there.