Air Asia is offering cheap flights to Seoul for this month. This is the cheapest fare ever for Seoul however it doesn't include bags, meals or seat selection. Checked bags are $105 each way ($805 total) which is ridiculous so maybe if you are there for only a week, maybe you can get away with no bags albeit it will be a bit cold there.
Book through Expedia where it's slightly cheaper.
Fwiw, Korean Airlines were $1000 on sale including 30kg return when I flew with them last year
Direct flights 777. Flight had every seat full too