Housed in a former pocketbook factory in Astoria, Queens, the tiny Baccalaureate School for Global Education is an elite public high school with a rigorous academic curriculum. Founded in 2002, it has only about 400 students, no gym, no playing fields and no auditorium.

Students who want to play on the school’s softball team, for instance, have to take two subway lines and then walk another 10 minutes to a remote practice field in Woodside. There is no bus to take them to away games against…