To experience Aboriginal culture you will need to head out of the city and into the Australian outback.
Australia is one of the most sparsely populated countries in the world, yet it's also one of the most urbanized. The Anglo-Australian culture is mainly concentrated in the cities, so if you want to experience Aboriginal culture you'll have to head out of the city and into the outback.
1) The most famous of the Aboriginal sites is Uluru (aka Ayers Rock). This is located within the Uluru-Kata Tjuta National Park which is situated in the southern reaches of the Northern Territory but it's pretty much located in the center of the continent. The Kata Tjuta National Park is a UNESCO World Heritage site and it covers 1326 sq kms. In addition to Uluru, the park contains many more mountains that share a similar appearance to Uluru but their origin is very different.
Uluru is considered sacred to the Aborigines. According to their creation myths, ancestral spirits formed Uluru, like a massive heart in the middle of Australia. They don't have any objection to people climbing the rock itself, but the path to the top does cross a sacred area. If you'd like to continue to climb anyway, it takes the better part of an hour, and there is a designated path with a chain hand rail to assist.
The best way to get to Ayers Rock is to fly to Alice Springs and then get a car and drive the rest of the way (about 450km!).
2) In Western Australia is a region called Kimberley. Kimberley occupies an area of 423,517 square kilometers (which is 3 times bigger than England) and it continues to be one of the last great unspoilt wilderness areas of the country. It was one of the first areas of Australia to be inhabited by human settlers coming over from Asia. In northern Kimberley you can check out the Gwion Gwion or Bradshaw Figures Aboriginal paintings, some of which are believed to be around 50,000 years old!
One of the main attractions in the Kimberley area is the Purnululu, which has a strange multitude of dome formations. It's also a UNESCO world heritage site. If you plan on visiting the area a 4WD is ideal.
3) In the northern end of the east coast, in the state of Queensland, there's the Daintree tropical rainforest. This forest is over 135 million years old making it the oldest rainforest in the world. There are about 430 species of birds living among the trees, including 13 species that are unique to this area! While here you can visit the local Aborigines, the Wujal Wujal people, who will teach you about bush tucker and how to fish for barramundi.
The town of Daintree, located close to the rainforest, is about 3 hours north of Cairns. The trip is definitely worth while - in addition to visiting the Rainforest you'll be perfectly located to check out the Great Barrier Reef as well.
4) In the state of South Australia, you can visit The Coorong National Park. The name is thought to derive from the Aboriginal word kurangh which means "long neck" and is likely a reference to the shape of the lagoon system. You can kayak along the lagoon and its waterways. You can get a Ngarrindjeri guide who will educate you about bush tucker, traditional medicines and the incredible local bird-life.
The park is located about 110 kms from Adelaide and makes for a great day trip away from the city.
5) Gippsland is located in Victoria near to Wilsons Promontory, mainland Australia's most southerly point. The Wilsons Promontory National Park was originally occupied by aborigines at least 6,500 years ago. Wander around the park and you can view beautiful rainforests, unspoiled beaches, as well as a rich wildlife including wombats, kangaroos, wallabies, koalas and emus. Visit Bairnsdale and watch the local Aborigines making baskets, spears, shields and canoes.
Gippsland is a large area starting just outside the suburbs of Melbourne and the Wilsons Promontory National Park entrance is 224 km from Melbourne.
6) Sydney is the oldest European settlement in Australia but they were not the first people there. There is evidence of indigenous Australian habitation for at least 30,000 years. When the first English explorers landed here and asked the locals where they were from, the locals answered 'Eora' which means 'from here'; so now the natives are called the Eora. While in the city you can avail of the New South Wales Sydney cultural tour which takes you on a trip to the past to landmarks, rock carvings and old Aboriginal settlements.