So this question can be answered in two parts, one concerning the geography of Australia, and another concerning the context of the 'discovery' and 'settlement' of Australia. Essentially, it comes down to how the two play together to present Sydney (or Sydney Cove) as the first place of European settlement on the continent.

Both the West and North coasts of Australia present their own geographical issues for any potential settlements during the 1700s. More specifically, both presented key challenges that the Eastern coast did not. The North coast is for the most part covered in tropical swamps and rivers, which did not lend itself to the creation of a 'productive' penal colony and would present considerable issues in terms of disease and land for farming. On the other hand, much of the West coast is desert that stretches out to the ocean, with large cliffs providing the coastline. This presented its own challenges, in that any settlement would find a significant lack of resources as well as a lack of safe ports to dock boats and ships. Comparatively, the east coast was far more flat (until one reaches the blue mountains), fertile, and liveable, creating a far more ideal situation for a settlement (this is also partially why the majority of Australians live on the East Coast). However, this isn't the whole story, as there is also the context of Australia's discovery which is important.

By the time the first fleet was on its way to settle Australia in 1788, the whole coastline of the continent hadn't been mapped. The entire coastline wouldn't be mapped until the expeditions of Baudin and Flinders in the 1810s. As such, the settlement of Australia was limited by the knowledge the people had at the time. The most detailed maps of Australia at the time would be those of John Bayley (1772) and Antonio Zatta (1779-1785), as well as Cook's own detailed sketches of the Australian east coast and the Endeavour River/Botany Bay. From these maps/sketches, it can be seen that for the most part, the only detailed knowledge the British had of Australia was that of the East Coast (this is perhaps most obvious on Zatta's map, where the names of coves and landmarks ends at Cape York). As such, this limited the available options for a penal colony.

To fully answer your question, these two parts need to be connected. It should be noted that while the context of exploration does go a long way to explain Sydney's development into Australia's largest city, Melbourne is slightly different (it was actually founded after Hobart, Brisbane, and Perth, as well as only a year before Adelaide). The reason Sydney and Melbourne would grow into Australia's premier cities is due to the geography mentioned earlier. The East coast represented a significant region for agriculture, and provided much more land for settlers to cultivate. At the same time, the context of exploration plays its part, as Melbourne's proximity to Sydney allowed for it to benefit from increased co-operation from the main hub of colonial activity in Australia. This also goes to explain why Canberra is the capital of Australia, as it was a compromise reached between Sydney and Melbourne during Australia's federation in 1901 (Canberra was only established in 1913, Melbourne was the provisional capital during the intermediary period). To summarise, a combination of time and geography led to Sydney and Melbourne (and the East Coast in general) flourishing, which is why Perth and Darwin weren't seen as Australia's 'main cities' despite their relatively closer proximity to Britain.

Sources Used:

- Lyall Gillespie. Canberra 1820–1913. Canberra: Australian Government Publishing Service, 1991.

- Brain De Garis, ‘Federation’, in Robert Manne (ed.), The Australian Century: Political Struggle in the Building of a Nation, Melbourne: Text Publishing, 1999.

- Stuart Macintyre, A Concise History of Australia, Melbourne: Cambridge University Press, 2004.

- James Cook, The Journals of Captain Cook, Melbourne: Penguin Random House, 1999.