This is kind of a random stream of thoughts here about what to ask at hospital, sorry in advance about that.
For some states you can look up C-section rates online, others you will have to ask the hospital.
You want to make sure the hospital is breastfeeding friendly. You can look at the guidelines for baby friendly hospitals, although I think there are some very breastfeeding-friendly hospitals that are not officially "baby-friendly" hospitals.
The hospital I had DS1 at was very supportive of breastfeeding but not "baby-friendly". They had this posted in all the rooms in L&D:
and we completely roomed in, all procedures/tests were done in our room and we had one nurse that would take care of us both.
I actually did not want to cosleep at the hospital (although I wanted to cosleep in general) because the bed made me nervous, it was elevated, narrow, in the middle of the room, and did not have full rails on it. I fell asleep once with him in my bed after nursing and the nurse just moved him to the bassinet while we were asleep and never said anything negative to me about it. I will be in a different hospital this time but I think if it is a similar setup I may try with baby in a ring sling.
Find out what they have for mom's comfort and moving around in the rooms - shower, tub, birth ball, squatting bar, etc. If there is a tub, will they let you give birth in it (my guess is probably not for most hospitals). Do they have telemetry units for monitoring so you can move around freely? Do they allow intermittent monitoring? When is continuous monitoring required? What about IV fluids? Do they support different positions for mom to push in? Do they allow delayed cord clamping? If you are interested in cord blood banking or donation, how is that managed? How is the 3rd stage usually handled? Do they allow immediate skin-to-skin contact and baby-led latching (assuming no medical concerns take precedence)? What standard procedures are done after baby is born? Can they be done in the room? If there are any health issues do they have a NICU unit or will baby have to be transferred? If you do decide you want an epidural after all, do they have anesthesiologist on call the whole time? How are emergency C-sections handled?
Do they have a template birth plan or will they accept your own written birth plan? Can you have a doula there? What is limit on number of support people you can have in the room?
What are policies on food during labor? Can you bring your own snacks? What will they provide? If you have any special dietary needs, will they be able to accommodate those?
I found at our hospital that the nurses were very supportive of our birth plan and as much as possible left us alone to do our own thing, but not so much with the on-call OB.
More of a silly one, but do they have wifi available in the rooms? Maybe less important now that we both have smartphones but it sure was nice last time to be able to email pictures to friends and family.