You probably want to know what the nurse/patient ratios are like, how long your orientation will be and will you have a consistent preceptor, nurse educator and/or mentor. You might want to ask what the turnover is like on the unit -- is it particularly high turnover? Do people stay there forever? If the turnover is especially high, it might be a bad sign that it's a miserable place to work. Or it might be because all their senior nurses just graduated from NP school, they've opened a new unit in a sister hospital and transferred half their staff there, they're the feeder unit for the local anesthesia school or the last manager was psycho and drove everyone off. Ask the interviewer why she thinks the turnover is so high, and then if you get a chance to talk to some of the staff ask them the same question and compare answers.
Ask about the typical patient population, whether they get a lot of admissions, discharges or transfers in and out each day, what your role will be like (do you work with an RN, do you work mostly independently, etc. You'd know more about what to ask in that regard.). How is scheduling done -- self scheduling or a committee or rotated among staff members or the manager does the schedule? What shifts would you be working, is shift rotation required and how often would you be rotating. How many weekends and holidays will you be responsible for? Every other weekend? Every third? One weekend every six weeks, or maybe three weekends every six weeks but it can be three weekends in a row and then three weeks without weekends? Does the charge nurse have her own patients or is she free to help out?
Is parking available onsite or do you park in a remote lot and take a shuttle in -- that's going to affect your commute. Ask when the shift starts and ends -- a 6am start would be miserable for me, but you'd beat the traffic in most cities. Who will do your evaluations -- the manager? Preceptor? Some other nurse yet to specified? What are the working conditions like . . . Does the unit have windows? That's a big factor for some folks. Are the rooms small and cramped or spacious? Small and cramped means you probably won't be walking as many miles in a day, but if you're claustrophobic it may be an issue. Ask if you can see the unit, meet the staff, perhaps shadow for a few hours.
Stream of consciousness, and not very organized but I hope you get some ideas.
If you're a new grad, we can teach you to take care of the patients. The nurse we'll hire is the one we want to be working next to.