Since World Cup matches don't happen every day, part of the stadium was turned into a retail complex with a 10-screen cineplex (the CGV Sangam 10). The field area isn't open, but you can tour the stadium any day of the week. The surrounding area has been turned into a bunch of different parks including Nanjicheon Park, Noeul Park, and Peace Park, with places to walk and, even better, for inline skating.
My favorite of these is Haneul ("Sky") Park, which is a reclaimed landfill that has been converted into a 192,000-sq.-m (2,067-sq.-ft.) ecological site and park. It's one of the few places in the city to enjoy nice views and the quiet of nature.