Kodak Express do C41, for B+W and E6 they post it to Atkins.
B+W are independent, they do B+W, C41, and E6.
Atkins claim to have the only Dip'n'Dunk, and the only Kodak Q-lab, in Adelaide, and they do up to 8x10s. They claim to be the best, they're certainly the most expensive.
Everywhere else around here that offers 'film processing' just post it to one of these three (mostly to Atkins).
I don't know about the other major cities, there's surely more labs in Sydney and Melbourne? We're only a small capital of maybe 1.5m people, Brisvegas/Perth are maybe 2m, Melbs 3-4m and Sydney 5-6m by now, so there's probably at least 10-20 labs spread amongst them.