For me the best korean director is Im Kwon Taek, but he makes art movies which are a little slow and contemplative. You can try : http://mydramalist.com/1741-chunhyang It's a pansori very famous in korea. I hope you will like it ;)
I really really liked Always (romance and melodrama, but beautifully shot) and My P.S. Partner (steamy romance, explicit sex scenes, very different from the usual fluffy rom-coms).
