I strongly recommend:
Hotelier (2001) : Song Yoon Ah + Bae Yong Jun + Kim Seung Woo (also + Song Hye Kyo)
It's the story of how a hotel staff tries to make it survive after the owner dies. Their worst problem is that a businessman is determined to buy the hotel and resell it. The love problem? The heartless businessman falls in love with the hotel manager, who is the one who most wants the hotel to survive. When they met, they didn't know who the other was.
*The love triangle is great and the main couple has great chemistry.
Piano (2001) : Jo Jae Hyun + Kim Ha Neul + Go Soo + Jo In Sung
It's the story of a totally dysfunctional family.
Two children fall in love and unintentionally make their parents fall in love too, then the parents end up getting married. The stepfather was a former thug, but due to he was hopelessly in love he has changed remarkably, however, being unable to compare himself with the late father of his stepchildren, they hate him to death. After an accident the mother dies, and the story follows the clumsy but well-meaning stepfather trying to raise the four children (he had a daughter with the deceased) and trying to be forgiven by his stepchildren, who are giving themselves to bad life.
*Great screenplay, great performances, powerful message.