I wish I had an option for things like doctors, facilities, etc. For my first, in the military, I saw different OB docs through the entire pregnancy, who were different than regular gyn docs seen pre-pregnancy, and ended up with a different doc for the birth, another doc when it went to a C-section, then different docs for each of the follow-ups. Only option for the hospital was the one on base.
For my second, through the VA, I was given the choice of a thankfully good hospital 30 mins away or a really crappy one an hour and a half away. They chose the doctor, but thankfully I was able to see her for all of my prenatal, C-section, and post delivery care. Once that was all over, it was back to the VA for any gyn-related care, which means any number of different docs that rotate in and out. Even my Primary Care Doctor changes every 2 years after they finish their residency.
I would definitely pick a doctor I liked over hospital amenities if ever given the choice.