What is worth doing with a 12-hour layover in Seoul?

It depends entirely on what you like, but you should first take into account that you should spend the last 2.5 hours getting back to the Airport and getting through security, especially if you are going to Incheon International (as opposed to Gimpo, which is a little closer to the city center). You should also take into account which hours and which days you are going to check what may be open or not.

If you like historical buildings, I would recommend going to Gyeongbokgung, which is the most impressive of Seoul's five palaces and the National Palace Museum there. This will probably take around 3 hours to see. If you wish to see the other palaces and/or Jongmyo Shrine, you are well-positioned to see them as well, but you may not have enough time.

If you like shipping and restaurants, I would recommend visiting Gangnam district which has lots of shopping and an incredible variety of Korean restaurants. (You can find restaurants anywhere in Seoul, but the more trendy ones are in Gangnam). This is also the namesake district of the famous Psy song "Gangnam Style" so that may be excitement in and of itself.

If you like Buddhist-style contemplation, Bongeunsa Buddhist Temple is almost always open for visiting and sometimes open for foreign visitor prayer.

If you like walking around outside, I would recommend Namsan Park, which encircles Namsan (the Southern Mountain). There is also Namsan Hanok Village in the park which is a recreation of what a Korean village would have looked like centuries ago.

If you want foreign (Non-Korean) food and entertainment, I would recommend Itaewon district, which is full of wonderful restaurants. (I personally like the Jordanian one, but my friends love the American grillhouses.)

If you are looking for accommodations, pretty much every district in Seoul is safe (there is practically no crime at all) and you should probably choose somewhere close to the district where you want to spend the night before going to sleep or close to Seoul Station to take the train back to the airport.
It depends entirely on what you like, but you should first take into account that you should spend the last 2.5 hours getting back to the Airport and getting through security, especially if you are going to Incheon International (as opposed to Gimpo, which is a little closer to the city center). You should also take into account which hours and which days you are going to check what may be open or not.

If you like historical buildings, I would recommend going to Gyeongbokgung, which is the most impressive of Seoul's five palaces and the National Palace Museum there. This will probably take around 3 hours to see. If you wish to see the other palaces and/or Jongmyo Shrine, you are well-positioned to see them as well, but you may not have enough time.

If you like shipping and restaurants, I would recommend visiting Gangnam district which has lots of shopping and an incredible variety of Korean restaurants. (You can find restaurants anywhere in Seoul, but the more trendy ones are in Gangnam). This is also the namesake district of the famous Psy song "Gangnam Style" so that may be excitement in and of itself.

If you like Buddhist-style contemplation, Bongeunsa Buddhist Temple is almost always open for visiting and sometimes open for foreign visitor prayer.

If you like walking around outside, I would recommend Namsan Park, which encircles Namsan (the Southern Mountain). There is also Namsan Hanok Village in the park which is a recreation of what a Korean village would have looked like centuries ago.

If you want foreign (Non-Korean) food and entertainment, I would recommend Itaewon district, which is full of wonderful restaurants. (I personally like the Jordanian one, but my friends love the American grillhouses.)

If you are looking for accommodations, pretty much every district in Seoul is safe (there is practically no crime at all) and you should probably choose somewhere close to the district where you want to spend the night before going to sleep or close to Seoul Station to take the train back to the airport.
It depends entirely on what you like, but you should first take into account that you should spend the last 2.5 hours getting back to the Airport and getting through security, especially if you are going to Incheon International (as opposed to Gimpo, which is a little closer to the city center). You should also take into account which hours and which days you are going to check what may be open or not.

If you like historical buildings, I would recommend going to Gyeongbokgung, which is the most impressive of Seoul's five palaces and the National Palace Museum there. This will probably take around 3 hours to see. If you wish to see the other palaces and/or Jongmyo Shrine, you are well-positioned to see them as well, but you may not have enough time.

If you like shipping and restaurants, I would recommend visiting Gangnam district which has lots of shopping and an incredible variety of Korean restaurants. (You can find restaurants anywhere in Seoul, but the more trendy ones are in Gangnam). This is also the namesake district of the famous Psy song "Gangnam Style" so that may be excitement in and of itself.

If you like Buddhist-style contemplation, Bongeunsa Buddhist Temple is almost always open for visiting and sometimes open for foreign visitor prayer.

If you like walking around outside, I would recommend Namsan Park, which encircles Namsan (the Southern Mountain). There is also Namsan Hanok Village in the park which is a recreation of what a Korean village would have looked like centuries ago.

If you want foreign (Non-Korean) food and entertainment, I would recommend Itaewon district, which is full of wonderful restaurants. (I personally like the Jordanian one, but my friends love the American grillhouses.)

If you are looking for accommodations, pretty much every district in Seoul is safe (there is practically no crime at all) and you should probably choose somewhere close to the district where you want to spend the night before going to sleep or close to Seoul Station to take the train back to the airport.