Star Alliance member Asiana is great for award availability. I’ve always had good luck with space on the West Coast – Seoul flights in business class, and beyond to Southeast Asia and first class availability — on the limited routes where it’s offered — is generally good too.
Right now New York JFK – Seoul is served by a Boeing 777-200LR with no first class. However the Airbus A380 returns to New York at the end of March. The A380 is available Frankfurt – Seoul as well.