ㅋㅋㅋ 네! 너무 멋있습니다!

Hm the first word that comes to my mind as a translation of "handsome" would have been 잘생긴. 멋있는 doesn't have to do with looks alone but more the general air somebody gives off. An action can be 멋있다 as well. So I guess it's probably somewhere in between "cool" and "handsome", similar to Japanese かっこういい (kakkouii).

Hi I live in soth Korea and cool is also accurate

Error in my first comment. I think I meant "fashionable."

the dictionary defines it as "매우 좋거나 훌륭하다"
or simply "really good or great"