This an interesting topic (and your suggestion is awesome, Big Ariana!). I might suggest a specific issue that could come up in such meetings: placements / job prospects. I find it extremely helpful to get a sense of the placement record, not just of the department itself, but of people working on a specific subfield. Of course, a more reliable source of information might be other grad students, but it's still interesting to hear professors' own assessment of their placement successes/failures. My experience is that they can be quite candid.