Hi @dbelle , welcome to the forum.
The private vs public debate is ongoing. When it comes to chemo (if you need it) there is no charge for treatment, regardless, but the oncologists themselves are a different matter. You are entitled to have your treatment at the nearest safe facility so you will need to figure out where that is. You also need to see your onc a day or so before, so if they are based in the city, you are stuck with going in to see them. Something to consider when choosing your practitioner.
Surgery is more complicated, many surgeons operate in both systems, so it can come down to where you want to have your surgery and how long, if you don't have immediate reconstruction, you are willing to wait. Out of pocket costs for private surgery can be substantial. I'd be surprised to find anyone outside the metro centre doing advanced recos, so you may be limited in choices there.
Radiotherapy, which will probably be your big ticket item when it comes to travel, is delivered through both systems, but only some centres bulk bill. Find out which one near you does and attach yourself to a rad onc there.
It's all very complicated, the navigation, but if you have had some experience it won't be all foreign territory. Good luck. Marg.