What would be a good set of topics for a quiz game?
Obviously this question has no correct answer, as it's completely subjective, but if you're just looking for an idea, I'd suggest making your categorical break-down theme based.

If you compare other popular quiz games, say Classic Trivial Pursuit and Jeopardy, the first is trying to cater to being a family game that everyone can play, so it makes its categorical breakdown along typical areas of interest for different types of people Arts people, Sports people, Science people, etc.   Jeopardy prides itself on cleverness and wordplay, so its categories reflect that.

Keep in mind that the act of categorization isn't sorting things into existing buckets base don obvious differences, it's about creating a differentiating metric and categorizing things based on that metric.  For example, if you restrict your set of things to visible objects, you have an infinite set of metrics like color, weight, size, density, use, origin, lifespan, etc.  One you choose a metric there's often a continuum within that metric which you must create arbitrary points.  For example, you take color and break it into Red, Orange, Yellow, Green, Blue, Indigo, and Violet.  Those categories now artificially group your world.  Of course, you could just as easily have chosen lifespan and grouped thing into "fleeting", "temporary", "normal", "durable", and "indestructible".  It's really unbounded.

So, what's your theme?  Is this about energy aliens, looking at a human world and trying to figure things out in terms that make sense to them?  Maybe the categories are "hairy" and "smooth".  With those terms in which category would you place "Key" and "Shoe" into?  Part of the fun is seeing how the category informs the question's answer.

One of the fun things about many board and card games with themes is doing just this trick.  For example, Magic the Gathering needs to thematically sort every spell and creature into a color, and does this quite well.