We say "Except for" as "제외하고, 제외하면, 빼고는, 빼고" in Korean. The museum is open daily except for Mondays. 박물관은 월요일을 제외하고 매일 개방한다. I like her except for the fact that she is over nice. 그녀의 잔소리가 너무 심한 걸 제외하면 그녀를 좋아한다. The room was silent except for the TV. 텔레비전 소리를 빼고는 방안이 조용했다. Except for sleeping, I studied all day long. 나는 잠자는 시간을 빼고 하루 종일 공부만 했다

A little more detail on those words. 제외하고: from 제외하다, where 제외(除外) is of Chinese origin. It is rather formal. 빼고: from 빼다 which means "take out" or "pull out". 말고 may also be used, but it's more like "not xx" than "excluding xx". 말다 means "forgo", or "stop doing something", from which 말고 derives the sense of "not ...". If you want to say "I like not this but that", you'd say "나 이거 말고 저제 좋아". Both 빼고 and 말고 are used widely, in both speeches and texts.