I think research on the private hospital and go for a tour for both private and public.

DH and I did that and we really liked private because it felt more like a hotel room rather than a hospital (i am actually very scared of the hospital smell).

WIth the private hossy, DH could stay the night too and that was great for us whereas public they kick the partners out at 8PM as well.
Heavily depends on the hospital I'd say. Our local hospital has a very nice room for people with new babies - its been redecorated and if you ignore the dated lino it is like a hotel room with nurse call buttons and a bed that goes up and down. They have a fancy foldup bed for partners to sleep on that was donated to the hospital by someone who didn't like the partner sleeping arrangements