The Australian state governments run libraries. These are wonderful facilities rich with valuable and historic materials dating back to the first ships. I have been to three of them and have been enthralled by the exhibits and artifacts. They also have study and reading areas and great wi-fi connectivity. In addition, and by no means least, they have very nice book shops. The Northern Territory library is in Darwin and the New South Wales Library is on Macquarie Street in Sydney; and easy walk from just about anywhere in the Central Business District. The street, and many other features in New South Wales, was named for Lachlan Macquarie a governor from 1810-1821.
The Smithsonian Journeys groups have had the great good fortune to visit the library and to see some of the historic documents that are housed there. There is always an exhibit of some sort on display and a visit is always a rewarding passage of time.
In reality James Cook and Joseph Banks are as much Australian icons as are Uluru (Ayers Rock), The Olgas, The Opera House, and the Sydney Harbour Bridge. Without Cook (and Cook without Banks) a great deal of the history below the equator could be very very different.