Translation:This school is big.
広い【ひろい】 is a bit more like "spacious" (sort of suitable here) or "broad" (both in the sense of shoulders and in the sense of knowledge, or experience) or "wide" (like a river), or "vast" (like a chasm). I guess it considers the distance between related things in a way.
大きい is "big" in a more straightforward way, usually referring to the size of a physical object, but also can be applied to sounds to mean "loud" or to numbers, or risks, or even in the sense of "profound" - basically all the ways we might use "big" or "large" in English.
Or more specifically why ookii was used for hospitals and banks but not for a school?
The translation could be ''This school is big'' but it is not entirely just that. These answers should also be correct. e.g. This school is ''wide, broad, spacious, large, vast, roomy''. 広いincludes all these meanings.