Some suggestions, which either I've used or people I know have used:
1. How do students at this school prepare for the USMLE tests? Do they form study groups? Does the school provide any assistance in this?
2. How collaborative is the student body?
3. What percentage of students got one of their top 5 choices for a match?
4. What is the average debt load of graduating students? How much financial aid assistance does the school provide?
5. Do students have the opportunity to participate in research at nearby institutions?
Before asking a question, make sure the answer isn't on the website. For extra points, phrase a question in a way that shows you've read the website thoroughly, such as "On the website it mentions that many students are involved in research at (whatever). Does (school) offer any support in finding these research positions, or do students do it on their own?"
Hope it helps. Good luck.