Hmm this probably belongs in the recommendation forum...
It always seems to me that characters in k-dramas (and it's particularly noticeable with the men) are just a bit too pretty and clean and smooth -- which is why I liked the style of the characters in Shut Up Flower Boy Band so much (actually, I loved pretty much everything in that drama), they looked more natural and rough and... cool ;) So I'm looking for that type of character too...
Unfortunately, I haven't come across many characters like that though... Also, although you specified korean or japanese, for some reason there seem to be more taiwanese shows with that kind of style...
First, there's this taiwanese drama I haven't watched, but judging from the pictures it really looks like she's rocking a punk look ;) : Hi My Sweetheart
The male lead in Devil Beside You had a rocker/biker style:
Then, there are also the male leads in Mars and and Why Why Love, that dressed like in Devil Beside You, but less extreme.
The male lead in the japanese drama Tatta Hitotsu No Koi was rather edgy/grungy;
And so far that's all I can think of!