Some questions I ask:
What are the best, worst, and most surprising things about working here?
What IDEs are used here? (Preferred answer: Something from JetBrains, Reasonable people can disagree answer: vim/emacs/eclipse, Warning sign answer: Notepad)
Would I be allowed to work on outside projects?
How is off-hours support handled?
This seems like the sort of thing that would have been discussed many times here, but I couldn't find it using hnsearch or google. If you have the search-fu, teach me your ways.