I'm still a fairly new grad student myself, so it wasn't that long ago I went through this. Oh, the memories - applications, recruitment visits, lab tours, lab tours, more lab tours, meeting professors, the agonizing choices. Good times. :)
Here's my take on the survey questions:
1. Where do you look for information about a department? What venues (internet, your current school, your current mentors, conferences, etc.) have been most effective in introducing you to departments that you might not know about otherwise? How important is the department's website in your decision to apply or not apply?
I know many of my peers applied to a bunch of grad schools (the maximum I've known is over 14), but I only applied to three programs. I applied based on reputation alone; I knew what the top school was in the U.S. and I checked the U.S. News report to find the 2nd. The third school I applied to was the best one in the UK. I did very little research into alternatives. I realize this is arrogant, but I'm trying to be as honest as possible for the survey...
2. What are your top priorities in a grad school department? For example, rank these things (and/or add your own): reputation of department/institution name itself, reputation of PIs and their science, types of grad support available (TAships vs. RAships), length of average graduate student time to PhD, attitudes of current graduate students, exposure to postdocs, friendliness of environment, stipend level, etc...
1) reputation (this will be my terminal degree, after all, the one people will look at forever after...)
2) funding available (my preference were the two places I got fellowships rather than an RA or TA)
3) the advisor (personality and style a good match to mine, good reviews from current grad students, established quality research)
4) the project (I really wanted something hands-on not theoretical, a rich array of resources to work with, and a serious cool factor to keep me interested)
3. If you were on the fence between two equally solid offers, what kinds of things could the recruiters do or offer to change your mind?
I had a really hard time choosing between my top two choices. The only thing the recruiters can really change on my list of four things above is the funding - so all other things being equal, I'm going where I can make ends meet. It would also be helpful if the recruiters suggest professors that I might not have thought of to visit during the recruitment weekend - in case there is a really cool project I missed.
4. On a recruitment visit, what are the most valuable and important parts of the trip? Should there be more time with PIs, or more time with students? How much do social receptions influence your feeling of a department?
The most important thing I did on the recruitment visit was visit labs, so I got a good idea of what projects were available. But my favorite thing to do was to meet the students. I really enjoyed getting to meet current students to ask about the culture of the school, which advisors are the best to work for, and other things like that. In fact, on my recruitment visit to the school I am in now, on Friday night the current women students in the department took all the prospective girls out to dinner. I had so much fun on that dinner - I was glad to see the girls were happy and cool and laid back, and I met girls there who I am great friends with now. One of the girls turned out to build robots as a hobby - and I thought that was awesome, I had never met another girl so much like me.
So the lab visits are the deal-breakers. If I didn't find an advisor and lab and project I liked, I probably wouldn't have gone to that department. The students and the social events are the tie-breakers. If I had found a project I was in love with at both my top places, I would have gone with the one where I felt more comfortable with the students and the culture. In my case, the place where I found the project and the place where I liked the students best happened to be the same place - so that's where I am now. :)
5. From afar, who seems more interesting and important to talk to: junior faculty or senior faculty? Do you want to see them give talks about their research, or do you want to spend more time one-on-one?
I was offered a fellowship with a junior, untenured faculty. I actually turned it down in favor of an RA with an established professor - I didn't want to have to be the guinea pig for a brand new professor trying to start their lab.
I'm torn whether I'd rather hear a seminar or talk one-on-one. On the one hand I would rather hear a seminar on their work, and then talk to their students to get a sense of how they operate. But then again, talking one-on-one is more personal and lets the PI get to know you as well, and I can always check their website later to hear about their work. I don't know. Personally I did about half and half.
6. Any other things that stood out as positive or negative from visits you have had, or departments you have looked at (without identifiers please)?
Getting the current girl students to take out just the prospective girls was a big plus. I've done this dinner three times now (as a current student twice, after the first as a prospective...) and I always enjoy it. Getting put up at a nice hotel was also a plus, it was flattering to feel I was being courted. Pure vanity on my part, I know.
The only negative I can think of is one department that had every minute scrupulously scheduled during the recruitment weekend. I couldn't wander off on my own and it felt a little condescending to include directions to the bathroom... But that's just my style, I like being independent. I wanted some free time to explore, but I know other students that really appreciated having everything planned so well.