I love any place that I can either walk my way around or scoot my way around on well marked and abundant public transport. Seoul is huge and so walking around generally got me around one or two neighborhoods. Luckily for me, Seoul has one of the best public transport networks I've ever experienced.
There's a great vibe in and around Incheon's Art Platform area. I loved the concept and the buildings, but I just wanted more. This is a great place to head for a quick hit of art just know it's small and you may not have access to a whole lot. Even with that said, I still think it's a worthwhile place to visit.
What else are you going to do when you are living for 10 days on a man made island in a hyper planned city near the airport? Go to the outlet mall, of course!