Wolmido was once a major harbour area, and it still gives Incheon a good dose of sea air. The island has a small park, a waterfront walking road, seafood restaurants, cafes, and ferry links to nearby islands.
It is not refined, but it is lively in the way Korean waterfronts often are. Pair it with Chinatown, which is only a few minutes away, and you get a compact old-port day.