Questions to ask a prospective pediatrician

[NewGrandma]

My daughter recently gave birth to her first child. He was born 11 weeks premature & is now 4 weeks old. Within the next few weeks we expect him to be discharged from the NICU and my daughter is starting to visit pediatricians. Her first appointment is tomorrow. Aside from making sure their personalities click I know there must be topics that she will wish she had asked about. Since it has been 24 years since she was born I want to ask recent moms for suggestions of questions that they should ask them. One that I can think of is how they handle after hours calls. I, personally am really picky about that. I think separate waiting rooms for sick and well children is best but think that is rare, at least around here. Are there things that you are really particular about at your peds office? What do you feel you absolutely must have (aside from a great doctor) and what do you just let slide? Thanks for your input.
NewGrandma