다녀요 (다니다) = 1) to attend or commute to (a workplace, school, etc), 2) to go around many places.
가요 (가다) = to go (to a single destination).
So you can say 저는 내일 학교에 안 가요 (I don't go to school tomorrow) to state a single case, and 우리 형은 은행에 다녀요 (My brother works at a bank) to indicate regularly going to a place for work or study.
다니다 can also mean going around and passing or visiting many places (similar to 돌아다니다): 밤 늦게까지 거리를 (다녔다 / 돌아다녔다 / 걸어다녔다 = I strolled the streets late into the night).