Answer:
Australia's major cities are its capital, Canberra, and the capital cities for each state and territory.
Although Canberra is the capital of Australia, it is relatively small in population.
Each of the state capitals are:
New South Wales - Sydney
Victoria - Melbourne
Queensland - Brisbane
South Australia - Adelaide
Tasmania - Hobart
Western Australia - Perth
Northern Territory - Darwin
Within each of the states are also several smaller, but significant cities. The following list is by no means exhaustive, but examples include:
New South Wales: Wollongong, Newcastle, Griffith, Wagga Wagga, Dubbo, Albury, Coffs Harbour, Port Macquarie, Goulburn, Tamworth, Orange, Bathurst, Katoomba, Lithgow, Armidale, Queanbeyan
Victoria: Wodonga, Wangaratta, Geelong, Ballarat, Bendigo, Warrnambool, Swan Hill, Mildura
Queensland: Cairns, Townsville, Mackay, Rockhampton, Bundaberg, Toowoomba, Gold Coast, Gladstone, Mount Isa, Caloundra, Ipswich, Maryborough
South Australia: Port Augusta, Port Lincoln, Murray Bridge, Elizabeth, Mount Gambier, Whyalla, Port Pirie
Tasmania: Launceston, Devonport
Western Australia: Fremantle, Bunbury, Mandurah, Rockingham, Kalgoorlie-Boulder, Albany, Geraldton
Northern Territory: Alice Springs, Palmerston