Incheon is South Korea's great west-coast port and the city most travellers meet first through the airport. It is easy to treat it as Seoul's transport appendage, but that misses the point. Incheon has its own story: an open port, Korea's only official Chinatown, old harbour districts, island ferries, and the polished future-city experiment of Songdo.
The best short visit stays near the old port. Chinatown, Wolmido, and the Incheon Art Platform sit close enough to combine into one strong walk, with food, sea air, warehouses, and colonial-era traces all mixed together.
Incheon is also much larger than it looks on a map. Ganghwa Island, Yeongjongdo, Muuido, and the outer West Sea islands can turn the city into a coastal trip rather than an urban stop. If you only have a day, choose one area and do it properly; crossing the whole metropolitan city by public transport eats time fast.