All of Australia's major towns have reliable, affordable public bus networks, and there are suburban train lines in Sydney, Melbourne, Brisbane, Adelaide and Perth.
Melbourne also has trams (Adelaide has one!), Sydney and Brisbane have ferries, and Sydney has a light-rail line.
Taxis operate in all major cities and towns, especially handy if you're having a few drinks out. However, not every city has a pool of mobile app-booked taxi drivers – yet.