When a family lands in Korea, the first day is not about “doing” Korea. It is about setting up the trip so the next six or seven days are smoother. If you spend the first afternoon trying to figure out luggage, transit, connectivity, and dinner while children are tired and adults are carrying too many bags, the whole trip starts with avoidable friction.
The better approach is simple: land, clear immigration, get connected, decide on transport based on the amount of luggage and energy left, check in or drop bags, buy the small essentials, eat something easy, and stop. That sounds unambitious, but for a family it is the highest-value use of the first day. It preserves energy, reduces meltdowns, and gives you a clean start for the rest of the itinerary.
This guide is written for a Singapore-based family traveler, which means I am assuming you may be used to efficient transit, compact cities, and booking everything online before you fly. Korea rewards that style of travel, but the first day still has a few local details worth planning in advance: airport rail versus taxi, T-money versus cashless cards, how to handle luggage with kids, and when to cut the day short instead of forcing a sightseeing start.