"There isn't a cinema near here."
Translation:No hay un cine cerca de aquí.
Any thoughts on the correctness or lack thereof of "No hay ningun cine cerca de aqui?"
That should be correct, except that is literally translated as, "There are no cinemas close to here." The difference is that you are using the plural instead of the singular. Duolingo SHOULD accept this sentence, though, because they have the same meaning, and yours is actually more useful.