I see you have 'God's Gift - 14 Days' on your PTW list and I can really strongly recommend that. It didn't have any romance. (*cough* Although, I bet Jo Seung Woo was trying to portray his character as having a slight crush. And it was adorable.)
'White Christmas' is short and sweet. Er, you know. As sweet as thrillers go.
If you like sitcoms, check out 'Unstoppable High Kick'. It does have some romantic relationships but with a large cast like that and the sitcom format, it's not the main thing.
'Misaeng' (Incomplete Life), a recent hit drama with no romance.
'School 2013', friendships and high school cutesy.
'Two Weeks', a man on the run. Action, action and more action.
'She is Wow!' for an oddball.
