What I did is look at local private hospitals that I would consider ( close enough, good reputation) etc, no point in me picking a hospital say on the Gold Coast when I live in Brisbane ( logistically wouldn't work for me)
I then looked at the oby that deliver at that practice and researched them ( they all have about me pages and google will help too). And narrowed it down. Some GP won't have a clue some will, so I would suggest doing your own homework too.
All private with maternity facilities have websites, and additional information can be sort from tours and contacting them.
As for public you'll almost be guaranteed to be sent to your zoned local hospital ( some exemptions) so look just google maternity public zoning for your area.
That in itself might sway your choice if you're not in a good public area