I think "mystery" is an abstract noun but I want to see your explanations.
Yes and no. While you can say something abstract like:
The old house was surrounded with an aura of mystery.
You can also say:
It was a mystery what happened to the owners of the old house.
Is this abstract? It seems to depend on personal opinion. "A mystery" defines a concrete set of circumstances, no less than something like "a meeting" or "a vacation". But you can't hold it in your hand.
I think you need to define what exactly you mean by "abstract", otherwise this question really has no definitive answer.