From Incheon Airport to Holiday Inn Seongbuk:

An airport bus stops right in front of the hotel Holiday Inn Seongbuk (Not to be confused with Holiday Inn Mapo).
At the Inchon airport, go to bus stops 3B or 10B, and look for a sign with destination to "Dobong, Gangbuk, Seongbuk, Dongdaemun, Seong-dong".
The fare is13,000 won (13 US Dollars). The 7th stop in Seoul is designated as "Holiday Inn Seongbuk". See Airport Limousine Bus Routes for Holiday
Inn Seongbuk for a detailed route map.