Don't know about now, but I was looking at jabs for myself at the beginning of April when I realised I was in 1B and then friends throughout April and May (this for AZ) and there was never a problem with getting an appointment in multiple places in central/inner Sydney at a couple of days notice.Do tell, as that is not the experience of too many.
Think of it as a Public Service Announcement on how to get the 'Golden Ticket' for those who are in Phase 1A or 1B in Greater Sydney.
I ended up getting mine in northern NSW (again same day appointments were available) but many other friends did their jabs in Sydney.