I’d highly recommend to do a little bit of hiking in Buhkansan National Park if weather permits. Gorgeous mountains with views of the city and I think one of the best things I did in Seoul.
Gwangjang Market is a lovely old-style shopping arcade with a pretty huge amount of street food vendors clustered in the east. Lots of fun local food to try out there and good vibes all around.
Yongsan and the video game alley there are pretty good, but don’t underestimate Kukje Electronics center and the various game shops hidden in underground malls around town!