Healer (action romance)
City Hunter (action romance)
Secret Garden (fantasy romance though there's a lot of push-pull)
Descendants of the Sun (realistic yet still a fantasy romance, again push-pull)
Reply 1997 (high school slice of life, romance, comedy)
Kill Me, Heal Me (psychological, romance mystery)
Pinocchio (mystery romance)
I Can Hear Your Voice (mystery romance)
Oh My Venus (realistic romance)
Innocent Man (revenge romance)
Sungkyunkwan Scandal is a good intro to historical dramas if you want to try them either that or a time travel drama like Queen In Hyun's Man or Rooftop Prince
there are also Korean versions of some of the dramas you[ve seen like To the Beautiful You (Hana Kimi), Playful Kiss (It Started With a Kiss), and Boys Over Flowers (Meteor Garden, though I think the Japanese version is best)