As a senior in high school, many were faced with the same two options, either to remain in Japan or study abroad for university. I actually went to two universities, that is, I applied two separate times, once during my senior year in high school and another time after I graduated and decided to leave my university in Japan.
I chose to apply to both Japanese and schools abroad. Since my school was based on an AP curriculum, I naturally wanted to study in the United States. In addition, I wanted to study at a university where a liberal arts education was already firmly established. This indicated to me that they could excel at both STEM and liberal arts disciplines. I applied to universities in the US but there were other students who went to Canada, Europe, or Singapore. It depends highly on the student, their goals, and concentration.