One thing I know for sure is that almost everyone who has been to Korea has been to Incheon. Incheon is a really nice place, that has a lot of history and new cities, but most people just know it for it's airport.
This past spring I made my way over to the new city. Was I catching a flight to some dreamy destination? NOPE. I spent the weekend in Incheon becasue that's where my good friend Chris lives. Since it only takes about an hour or two to get from Seoul to Incheon, I like to go there to visit her. It gives me a chance to get out of the city and explore new areas.
Plus Incheon is home to one of my favorite places in Korea: China Town! China Town is where I'm told Jajangmyeon originated. When people from China first came to Korea they settled here and tried to make their favorite dishes using what was available and *boom!* Jajangmyeon was borrn. I have no idea how much truth is in this story, but I do know that Incheon China Town has some of the BEST Jajangmyeon I've ever had.
A "short" walk from the restaurants is beautiful Jayu park. This park, also know as freedom park, has a lot of beautiful trees and flowers. It also has a statue of General McArthur and commemorates the landing of an amphibeous landing in Incheon during the war. Srping is one of the best time to visit the park.
From the front gates of China town, you can catch a bus to take you to the beach.