This is a Korean War Memorial, but I don't know where it is.

there's writing on the memorial. could you enlarge that?

I tried, but all I could see was that it commemorates the first engagement of UN troops.

The first ever engagement took place in the Suwon (or Suweon) area south of Seoul. The Task Force Smith led by Lt. Smith, dispatched from Japan, had the first contact with the invading Communist North Korean troops near Suwon. The memorial may be in the area. Did you ever go to the Suwon area?

Kyujik

Kyujik:
I stayed on Suwon AB when I was in Korea.