In no particular order, here are some things I'd ask:
How easy or hard is it for you to get face time with your advisor?
Is it difficult to get funding for research needs, like data, software, travel?
Do you have opportunities to present your research? How often? Who gives you feedback?
Do faculty members co-author with students? Which faculty members?
How well are first and second year students integrated into the department? How/by who are they advised before they have committees?
How are you expected to learn the "tools" of research like STATA, MATLAB, and other programs if you don't know them already?
Are there any fields where the professors are really helpful to grad students? Where the professors are particularly bad about helping grad students? What fields are perceived as "strong" or "weak" within the department? Are any faculty members planning to leave soon? (Also -- if you know you want to work with one specific person, it is ok to ask about that person, how he is with grad students, etc.)
How often are classes canceled/not offered for lack of enrollment or lack of faculty?
What resources/opportunities outside of the econ department do students take advantage of?
What are some examples of research that current students are working on? Do students talk to each other about research?
Are students competitive with each other? Do grades matter? Are students ever required to repeat core classes?
What are the requirements for reaching candidacy?
What did you do the summer after first year/second year? When do most students start working seriously on research?
What is your usual schedule? How many hours a day do you spend at school? Weekends? How social is the department? Do people hang out together outside of school?
Where do first year students study? Do they have offices? What are the first year classes like? Are they well taught? Do they turn out to be useful?
Basically, you want to get a sense of what your life would be like if you were a grad student at _____ University. And remember that while placement is very important, it's also a long ways off. When comparing similar schools, think about the quality of the experience in the first couple of years. Even when the ends justify the means, you might as well pick the best "means" possible. Try to get a sense of the department as a community, and figure out where you'd fit in to that community.