Do try out their MRT system, very comprehensive and you can reach many attractions- e.g Dongdaemun or Namdaemun, Myeongdong, Geongbokgung, Gangnam, etc.
Consider trying skate (fermented stingray), very pungent but after taking one piece, drink some beer and your beer will feel very different.
Or try raw flower crabs in Kimchi sauce and it is a free-flow side-dish in premium BBQ restaurants.
The above are poor-people's food during the early days. If the above-mentioned are too adventurous for u, just add soju to your beer and get high before dinner is served.