Our VP keeps office hours every week (even more so recently because of the layoffs announcement). However, I see (and he often complains) that people do not utilise those, perhaps because people do not know what to ask.
I see this as a wonderful opportunity to learn from the senior management (as well as build some visibility). However, I myself am not sure how to utilise them so that it is not a waste of their time.
I have utilised them once and it helped me understand what the work expectations look like from our VP's perspective as well as his insights on growing fast. But, I am not sure if I did it right, and any perspective on this would help.
However, I see (and he often complains) that people do not utilise those, perhaps because people do not know what to ask.
This is very interesting to me - I imagine a ton of people would love to cozy up to someone at this level, especially in a company with so many career-driven, ambitious people like Google.
If there's not enough people showing up, this is a good opportunity for you to build social capital with someone who is extremely powerful and important. If these office hours are in-person and you're like the only one who attends, you can even ask them if they ever want to grab lunch or a coffee. If you can grow this relationship into something more organic that transcends the bounds of the structured office hours, this is a home run for you, especially as an L3.
In terms of what to say, it's important to remember that this person is operating at a very high altitude. Your goal should be to steer the conversation more towards high-level, systemic issues instead of the nitty-gritty "on the ground" stuff you're working with as an L3. Also, since you're an L3, I imagine that this person would be very impressed if you merely asked a good question here and there - You shouldn't feel pressured to say some genius, super insightful thing (this will be especially difficult as an L3).
Here's some resources to help with what you can talk about:
David had a good perspective about utilizing skip level 1:1s here -- many of those ideas wqill apply to this question.
The unique perspective that the VP has is a broad view of your organization and how it fits in with other parts of the company. This VP probably hears about (and has to deal with) the most urgent fires across the whole company. So just asking about their concerns and priorities is very instructive.
Another think to ask about is open-ended questions on an interest you have. For example, "I really care about privacy work but I don't feel like we ever properly allocate time for it. This is leading to X and Y issue -- I'm wondering how you think about that?" This is effectively a soft challenge on the org priorities, but, if done respectfully, you can gain credibility and trust which will be valuable for your future career.