The Arabic sentence is unnatural. We say (مدينة كبيرة). We can describe the streets of the city saying (شوارع المدينة واسعة), but we cannot use (واسعة) to describe the city itself. It does not collocate at all.
I agree. For me (even though I'm not a native speaker) wâsi3 means either wide or ample (as in some Quranic stanzas, "ample/widespread mercy", raHma wâsi3a, Q 6:147)... an-nahr an-nîl nahr wâsi3 jiddan... etc etc.
I think waasi3a should be translated as "vast" - rather than "spacious" - in the case of cities or countries or other vast open spaces.
"Spacious", in English appears more appropriate to smaller enclosed quarters, like a car or a house. - A university, which covers vast campus grounds, is not spacious. Its mensa or its auditorium or its dormitories may be spacious, but not the university as a whole institution.