Australian Museum Online, Albert Chapman Collection
Australian Museum Online, Geology in Australiam Museums
Australian Museum Online, Minerals and Rocks
Burra Open Air Museum, Victoria
Burrum Mining Museum, Torbanlea, Queensland
Crystal Caves, Atherton, Queensland
Don Rhodes Mining Museum, Port Hedland, The Pilbara, Western Australia
Edward de Courcy Clarke Geology Museum, University of Western Australia, Perth; see also here  
Emmaville Mining Museum, New South Wales
Geological Museum at Upwey, Victoria
Golden Dragon Museum, Bendigo, Victoria (gold rush collections)
Goldfields Mining Museum, Western Australia
Gold Mining Museum, Gympie, Queensland
Grubb Shaft Gold Mining and Heritage Museum, Tasmania
Macleay Museum of the History of Science, Geological History, University of Sydney, New South Wales
Mining Hall of Fame, Kalgoorlie, Western Australia
Museum of Victoria, Mineralogy & Petrology Section, Melbourne
Nambung National Park, Jurien Bay, Western Australia (limestone pinnacles)
Newcastle Regional Museum, Australia (dinosaurs, minerals, mining, earthquakes...)
Queensland Museum, Paleontology and Geology, South Bank near Brisbane
Queen Victoria Museum and Art Gallery, Launceston, Tasmania (fossils, dinosaur club); see also here and here  
Richmond Marine Fossil Museum, Richmond, Queensland
Riversleigh Fossil Centre, Mount Isa
South Australian Museum, Department of Earth Sciences, Adelaide (fossils including Ediacaran fauna, minerals, meteorites)
     with Opal Fossils of South Australia  
Sovereign Hill Gold Mine Museum, Ballarat, Victoria
Tabourie Lake Museum, Ulladulla, New South Wales (minerals)
Tasmania Mining and Minerals, information about miming towns and collections
Tasmanian Museum and Art Gallery, Hobart (includes collections: mineralogy, petrology, geology, fossils), see also here  
Tate Geological Museum, University of Adelaide
Wave Rock, Hyden, Western Australia (a place to visit)
West Coast Pioneers' Memorial Museum, Zeehan, Tasmania (mining history collections)
Westlakes Mining Museum, Teralba, New South Wales
White's Mineral Art Gallery and Mining Museum, Broken Hill, New South Wales; see also here