Jeondeungsa is one of Incheon's strongest historic sights, though it sits out on Ganghwa Island rather than in the dense city. Its Daeungjeon hall is a protected Korean treasure from the mid-Joseon period, known for detailed wooden carving.
It needs more planning than Chinatown or Wolmido, but it gives Incheon a deeper historical anchor. Go when you have enough time for Ganghwa rather than trying to squeeze it into a short airport layover.