I would say if you have never been to Seoul, then come on in just to get a glimpse of the city. Culturally I think most palaces and such will be closed by the time you arrive in the city. But there is always Myeongdong 24 hour shopping and other areas of interest.

If you are coming from LA, then with the time change, waking up early the next day to catch your flight should not be a problem. Just be aware that mornings at ICN airport can be a zoo with lots of people arriving and going through security to their flights.