The War Memorial is located in Yongsan-dong and pays tribute to the military history of the Republic of Korea. Of course WWII and the Korean War in particular play a key role, but there is a lot of other stuff to see here too, going back all the way to prehistoric times.
Outdoors, there are multiple monuments paying tribute to Korean soldiers and so on.
There are also a bunch of historic airplanes, tanks, ships, and other military equipment:
After that, you can enter the main building to look at exhibitions. There is a large free military exhibition. I think there was also some art exhibit, but I didn’t check it out. Furthermore, they also had an exhibition on the Berlin wall, but it was closed as well. Either way, I didn’t fly all the way to Korea to go into an exhibition about Berlin of all places.
The military exhibition is quite large and pretty much covers everything from (pre)historic weapons, to historic conflicts sorrounding Korea, to modern wars like WWII, the Vietnam war, and the Korean war. There are also multiple memorials, e.g. for the UN soldiers that died in the Korea war.
All in all, it’s a pretty interesting sight to visit. I’m not exactly a big military nut, but there’s a lot of stuff to see either way. If you really care about this kind of stuff, then it’s probably a must visit. And it’s all free, so you can’t really go wrong with it.