Known as Seoul Olympic Stadium or Jamsil Olympic Stadium, this ... um ... stadium was built for, well, the 1988 Olympics. Construction started back in 1977 and it was completed in 1984. It served as the home for the 1986 Asian Games before the Olympics came to town two years later. It's seen sporadic use since then including concerts by Michael Jackson, Metallica, and Lady Gaga, though a new professional football team is expected to move in next year.
Behind the stadium is a small collection of shops that seem to exclusively sell exercise equipment and sporting goods. In that "mall" is a small, free Olympic museum. It's called Seoul Olympic Exhibition Hall.
Jamsil Olympic Stadium is located outside exits 6 and 7 of Sports Complex Station on Line 2 of the subway system. The baseball stadium is closest to the station, but the Olympic Stadium is very visible just beyond it. Jamsil Arena is to the right of the Olympic Stadium behind the Students Gymnasium and what I think is the Olympic pool; the shopping area and museum is on the east side of the Olympic Stadium underneath the car park. Star Street is in front of the Olympic Stadium, leading toward the shopping area.