On a 14 hour layover in Seoul, its worth leaving the airport and seeing the city. It will take 1.5 hours to leave the airport, and another 1 hour to get to the center of the city. So 14 is now down to 11.5 hours, and when you take into consideration the way back, you are left 9 hours. Yes, it's worth it, but anything less, probably not.
Exchange money at the airport, you won't need more than $80 / pp for a whole day including transportation. Get maps from the tourist kiosk. Take the fast train to Seoul Station, do not take the regular train. Note the gas mask cupboard in the train station. Just in case, their neighbors to the North try something. Get the train schedule so you can time your return.
I did walk to all the venues below. You could take cabs and move alot faster. I like to walk. From what little I saw, Korea is a very modern city, resembling Tokyo, but with alot less ancient / medieval buildings. They don't seem to have made it through time. Nonetheless, it's charming and people are very helpful.
First visit the traditional market "Namdaemun Market", traditional food stalls against a backdrop of shops selling Korean goodies, like Ginseng, to souvenirs to clothes.
Near the market is Sungnyemun gate, which Koreans consider their number one monument. The city is coveted with modern sky scrappers, making these ancient monuments a rare commodity in the developed country.
Off to Myeongdong, a shopping area which is very similar to Japan. You will find tourist gudies wearing red outfits and a red cowboy hat. They are helpful telling you which stores to visit, there first recommendation was the hello kitty cafe, i'll pass. Then there was a cafe where you can pet puppies, ill skip that. The third option was a K-pop recommendation, and thank you very much for your help, but I'll figure it out from here. Didn't stop anywhere except at a food stall and got some fried octopus dipped in seaeme oil and hot sauce, which was good, but nothing to rave about. They have some kind of traditional sushi made of seaweed, that was better. Coffee at the stalls was pretty good as well. I made a stop at Myeondong Cathedral during Sunday mass. Didn't stay long, but I wouldn't go out of my way to see it.
You close to Deoksugung Palace, take a look from the outside, then, if you have time, take a cab to the Seoul tower, with a great view of the city. Something I didnt have the time to do.
Went to an old temple with a large bell called Bosingak Belfry, if you hit at the right time, there will be a show with actors dressed in traditional Korean attire and holding medieval weapons. Off to Tapgol park, which has a large ancient tower encased in a glass building. Park is pretty tranquil. Jogyesa temple isn't far and worth seeing with its intricate art work, many colorful lanterns and flocks of worshippers. Entry isn't alloweed with cameras.
Then off to Insadong, another huge shopping area. Great view of the mountains and artistic shops selling Korean arts. Now for a meal, found an amazing -off the beaten track- dumpling place that sell Mandu Dumplings, the best I've ever had. It's in a small alley way off the major Insadong st. It is buzzing with locals, and despite not knowing the name and no English menu, found a website with someone raving about the place. You order off the pictures, I would go with a mix of steamed and fried dumplings. Here is the link. Other foods to try, Bibimap and Kimchi (cabbage and squid)
After a meal like that, and looking at my watch, it was a day well spent. Time to head back to the airport. Take a cab to Seoul station and take your fast train back.