I can't speak to Tokyo.
The subway is the absolute best way to get around Seoul. I did not drive there. The Airport Express is connected to both Incheon and Gimpo Airports. However, the times I took either a city of nice bus the traffic was awful. Remember that urban feel of Seoul is that of Wilshire Blvd in Los Angeles, except populated with four times the density of LA. I'm not sure where your cruise will go into/out of. Didn't take cabs. Unlike in Rome, there are no designated taxi ranks.