I divided up my questions.
At the dinner, I usually talked about the day to day running of the program, and what the patient pop/workload/team/call is like on each of the main rotations, and also about what the residents do for fun.
On the hospital tour, I ask about procedures, electives, and the relationship with the hospital staff and local docs. If I run out of questions, I ask what they do for fun.
At lunch, I ask about didactics, CME, how some things are taught on the wards, when residents have opportunities to teach, and, of course, what they like to do for fun.
At the clinic tour, i ask, um, questions about, yep, clinic. And if I run out...
There seems to always be an interview with the behavioral specialist - so I ask him/her about the community medicine education and what opportunities to work with underserved populations, do home visits, or anything else unique I read about on their website.
Each faculty gets assigned a basic topic based on their profile on the website, or randomly if I didn't get to know who I'd be interviewing with ahead of time. So one person gets asked about the rural training, international or away electives, OB and the relationship with the local OB docs, etc.
I always ask the same 8-9 questions of the program director, and I save them for him/her so that I am not out.
So, again, when I am out of questions, I always ask about things that will make the residents (hopefully) smile or feel happy, and talking about fun things, how the area is for families, etc or about things that they can sound like helpful experts in, like housing is where I go to. So far, I've had six interviews and have always had a few questions for everyone. I do repeat sometimes, but not if I haven't asked all of my questions yet, and not if I haven't learned something personal about the person that I'm with that lets me know more about them as a person rather than as just some dude interviewing me.
Who knows if this is useful for anyone else, but it helped me to always hit all of my important points, to always have something to ask about, and to not draw a blank at the beginning of an interview if I am asked "Do you have any questions" right after I sit down.