Your budget very high

Sure can stay many hotels.
Can stay around seoul station.
They have a direct train to incheon airport.
Have booked newly opened 4 stars skypark dongdamum @ 75sgd per nite that time. But have seen best western premier gangnam at lower price, so faster book that, and then change my booking to best western premier gangnam ...
We took train to gimpo airport, then change to another line to incheon airport. Because our flight was at 2am, so we have to take train abt 1hr plus, instead of taking a cab which was abt 65 to 80sgd ...