Presumably you've discounted for personal reasons but I'd say HKG is your best option for a long weekend in that part of the world. Get the earlier of the 2 evening BA flights out which (about 1830 from memory) which allows you to enjoy a relaxed dinner and a couple of films on the outbound plus allow you to sleep for 7+ hours arriving HKG just after lunch. Easy transfer to your hotel using the airport express to get in a swim to refresh before heading out for the evening. You are then refreshed and 'in the time zone' when you wake up in the morning for a good couple of days seeing the sights/experiencing HKG before getting an overnight flight back (or the day time flight to maximise the F experience)

Other option would be to wait until ICN is running.