So this post is probably too late to help anyone, least of all me, but I thought I would gather my thoughts now while they are still relatively fresh. It might also prove interesting to contrast my impression not with my feelings in a few years.
In this list I assume the goal of going to Grad School and getting a PhD is so that one might go on to teach at a tier one research university. If the purpose is to go find a lucrative job or teach at a small liberal arts school I don't know that I am addressing that directly.
1. How many faculty members are there in your department/subfield? Are there strong supporting departments?- While people often encouraged me to look at programs with a particular faculty member I liked, one can never be sure that things will work out with one individual. I firmly believe that the information one can glean about particular instructors during the application process can not significantly predict whether or not you will be able to work closely with them. Obviously one should look for a program where the faculty members share similar interests to your own, but it is important to keep in mind that, even if you could ascertain a current ideal instructor, grad school is formative and thus one is likely to change interests and focus.
To this end, it is nice to have many different sources of critique. Go to a program where you are going to find a number of strong voices. If there are other prominent departments in the university which are associated somehow it will help spread out coursework and provide other influences for your work and on your committee. Try not to put yourself in a program which will have you hitting your head against blunt objects e.g. you like Derrida and Foucault and the faculty is heavily Straussian.
2. What people think of your department- Coming out you will be assessed based on your work, but also the program you are coming from. If people think the department is good, it is. I was shocked how many people in Political Theory programs are under the impression that Chicago still has a good theory program, even though it has been sparse for 30 years! (Robert Pape and John Mearsheimer do great work, but theorists they are not. Social Thought gets all the good ones.) If you do wind up selling out (the lucky ones) a degree from Yale looks a whole lot better than a degree from Michigan. The sad part is, it is often the case in the academy too.
3. Do people know your professors?- This can be assessed in two ways, either by asking people in your field, "Hey, have you heard of Prof. Blank?" or by looking at their CVs. Pay attention to how many articles they have published and in what journals. If they have published books, under what publishers? If a few people in your department have Cambridge or Belknap, you are doing OK.
4. Can you talk to the students?- From my understanding, professors are busy people (or they think they are, which is very often the case too) and so you will probably spend a lot of time thinking things through with your peers. If they don't seem like they want to talk to you or ask the same sort of questions you do, be wary.
5. Happiness index- Grad School is a long while, and if you are Melancholy you probably won't think or write. Ask the grad students if they are happy, they will all say yes, but their qualifications will then be interesting. Try to avoid urban environments which will make you sad, or climates that you don't like. Don't forget to factor in your stipend into your standard of living. A warm, sunny apartment in Philadelphia might produce better academic results than a cold basement on the West Side in NY.
It is a given that you have to work endlessly to get the most junior appointments in the academy. It won't hurt to have a supportive program in the process.