But, my favorite generic question is "what keeps him or her up at night?"
Why?
* People generally love to talk about themselves, VPs included.
* It shows you are thinking about the big picture.
* It gives him or her the chance to talk strategically.
* It might give you some insight into current problems the VP thinks is or will be interesting/important to the org.
I'm sure most VPs have multiple things that keep them up at night, so I'd expect them to pick one they could legally disclose :) .
If they do talk about something that will get them in legal trouble, well, that's a good piece of data to have about your company (they have a VP who might get in legal trouble).
And probably, if they're good, pick one that is relevant to the person they are in conversation with. So not "I'm worried about my aging father and his health" and more "I think that these zero-days are going to become more and more common", etc etc.
What books or periodicals should I read to understand more about the company's industry, domain, and history?
What areas of IT are the biggest pain points for the company, in terms of either revenue or expertises?
How is the success of IT measured and rewarded at the senior executive level?
Most companies produce a great deal of information about operations and status, but it can be heard to know which kinds and sources are the most valuable for knowing the real state of the company. Ask how the VP keeps up to date with the most important company directions.
what metrics or signals are most helpful to him in understanding and communicating the value that your department is delivering? - align yourself with the stuff he can actually use