I suggest asking the following questions, either during your visit to the campus or when you are invited to do so by the admissions committee.

On Placement

• What is the placement record over the past 5 years?
• How many students land academic jobs vs. other types of positions?
• How have recent graduates performed in your specific area of interest?
• Does the program have a placement service? What kind of support can you expect during the placement process? Does the department provide a stipend for printing, mailing, etc. during placement?

On Graduate Student-Faculty Interaction

• What kinds of mentorship relationships/institutions are typical in the department?
• Do faculty tend to co-author with their students? How often?
• How often do faculty hire graduate students as research assistants? What kinds of projects are typical, and what are the typical duties of the RA?
• Do I choose an advisor, or is an advisor assigned to me?

On Professional Development Opportunities

• Are there opportunities for graduate students to present their works-in-progress to the rest of the department?
• Is there frequent faculty guidance on the following topics, through colloquia or brownbag lunches?
  • Methods and technology
  • Time management
  • Attending conferences
  • Networking
  • Writing for academia
  • How to write an article vs. how to write a book
  • The dissertation
  • How to get predocs and postdocs
  • The academic job market
  • How to teach political science
• Does every grad student get the opportunity to do practice job talks at the department before their first job talk?

On Financial Support and Benefits

• How reliable is the financial offer I have received? Is the university in a stable enough financial position to honor its commitment?
• Are there opportunities for summer support? What do most graduate students do with their summers?
• Does the department or university provide travel funds for graduate students to attend professional conferences?
• Is the cost of living manageable given the graduate student stipend?
• How many graduate students take out additional financial aid? Is this in the form of loans, scholarships, or grants?
• How are the health benefits? Will I be limited in the type of care I receive, or is there flexibility?

On Research

• Are there competitive grants within the university for graduate students to apply for to support their research?
• Are there dissertation writing fellowships, which release graduate students from TA or RA responsibilities to focus on writing? How often do students in this department get such awards?
• Do students and faculty have positive experiences with the university grants office? For instance, if I wanted to apply for an NSF grant to support my dissertation, is the grants office more of a help or more of a hurdle? What about the Human Subjects Research board?
• At what stage in their education do most graduate students begin applying for grants, predocs, and postdocs?

On Department Intellectual Life

• How often are guest lectures available for graduate students to attend?
• Are there social opportunities or regular social interactions between graduate students and faculty?
• What is the department culture? Are people on a first-name basis, or is it more formal?
• Is there interaction with other departments (i.e. Econ)?

On Expectations of Graduate Students

• What are the major requirements/milestones?
• Describe the process for comprehensive exams. In how many fields do graduate students specialize? Are the comps administered all at once, or over a longer period? Are they take-home or in-person? Are there both written and oral components?
• What do most graduate students do with their summers?

Questions to ask the Graduate Students

• What do you know now that you wish you knew before you got here?
• Do you have any complaints about your experience?
• Are there departmental norms or hierarchies I should be aware of? For instance, when guest lecturers give talks, or candidates give job talks, are graduate students encouraged to ask questions during Q&A, or is there a sense that faculty questions get priority?
• Where do most graduate students live?
• What do people do in their free time?
• Who are the most accessible faculty? Anyone to avoid?
• What are the best things about living there? What are the worst things about living there?
• How easy is it to make ends meet in the area on a grad student budget?