Stay: I was staying at a youth hostel near Hongik University.
Seoul is extremely well connected with a very nice subway train network and is fairly easy to use even for someone with no knowledge of Korean. They have signs in English. Get a subway map and you want to go to Gwanghwamun Station, if this is your first time in Seoul, this was the starting point of my Seoul adventure,
Once out side the Gwanghwamun station you will see The statue of Admiral Yi Sun-shin and The statue of King Sejong. There is a tourist office nearby outside the Gwanghwamun station, If you have limited time, my advice is to use the tourist buses, they have hop on hop off buses and they run every half an hour. I took 3 tours on different days, Night city tour bus, Market Tour and Downtown Tour.
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Namsan Tower at Night, picture I took below was on a night tour of the city.
Airport Seoul: On My First Visit to Seoul, I took the bus from outside the Airport to the city, on my 2nd visit I took the subway train.
Above: Monument To Admiral Yi Sun Sin, South Korea