Suggestions on places to go in Seoul

Hi. I am going to SK in 3 weeks time. I'd be going with the tour for the first 6 days inclusive of seoul and jeju and we have 3 more days for free and easy like for shopping or going to places we want to visit. I was told that I could plan the itinerary for the 3 days but I'm literally stucked! I only had Trick Eye Museum in mind as it's a very interesting place to go. So is there any more ideas? I would be living near myeongdeong(popular shopping place I heard) and I'd also like to know what foods are recommended to eat!