Budget Travel - 12hr stopover in Seoul - what to do?

My sister-in-law and her husband are flying from LAX to BKK to visit us. They've managed to get a trip with frequent flyer miles but it involves a 12hr stopover in Seoul each way.

They are not frequent travellers and they don't have a big budget so what would you recommend them to do in 12hrs? Fortunately, they are daytime hours that they are there.

I've only been to Seoul a few times, always on business, never longer than 36 hrs. I know that they can take the Limousine bus from the airport to downtown but are there better alternatives? What should they see, do, etc.?

Thanks for any suggestions to make their trip more interesting! ^

Take a guided bus tour. Alternatively, take the KAL limousine bus to the Bus Terminal if you want to be on your own, and venture to Itaewon or Gangnam for shopping. More details can be found here (http://www.flyertalk.com/forum/showthread.php?t=409748).

More details can be found here (http://www.flyertalk.com/forum/showthread.php?t=409748).
Thanks for this link. I typed the original question quickly this morning and forgot to search that sub-forum properly...

I'm checking the Asia sub-forum now but if anyone has any particular budget tips, they would be appreciated. ^

If they chose to stay in, they can get a room at the transit hotel at the airport.