Thanks for the suggestions, lads! I have been in Seoul for 1 week but only had time to explore a bit today. I went to the War Memorial, Namseong Market, Little Russia near Dongdaemun and finally Tongin Market. Surprised to see shops closing early at Tongin (I was there around 6 pm) but I did grab some food before heading home.
On tap tomorrow is probably Dapsimni Antique Market and Moran Market. Seoul Fortress for Thursday and yes it's real humid now. I don't perspire a lot but it's pretty nuts out.