Yes you are right though it is not a word that is often used. It did seem a bit odd writing stadiums in this sentence. I think you would be more likely to use the singular. The city "has no stadium" or "does not have a stadium". After all, if it doesn't have one, then it can't have more than one!.
I wrote "stadia" which is the plural for stadium. Mirriam-Webster says both "stadiums" and "stadia" are acceptable. Someone commented on this very thing 5 years ago on this thread. And here we are in 2018 and I was still marked wrong for typing "stadia". Duolingo continues to insist on only using "stadiums". Is Duolingo paying any attention to anything any of us write on these threads?
Very often in previous lessons, DL has translated an Italian plural noun into an English singular noun, because that way the English sounds more acceptable. In English one would NEVER say "does not have stadiums", but one would say "has no stadium". In fact, we rarely use the word stadium, but that's another matter.