Do check out their limousine buses! it's really convenient and it's affordable at around ~$15,000 won. I have 2 links here that might help:
https://blog.bnbhero.com/airport-bus/
https://www.airport.kr/ap/en/tpt/busRouteList.do
They have many bus numbers available that brings you to different parts of Seoul. During my trip, I stayed around Sinsa during my trip so I took bus 6009 from airport T2 to Sinsa station. I purchased the ticket from the counter and it costs $15,000 won. The bus accepts T-money card too so I would suggest you to purchase one