Australia is a fairly new nation from a western point of view. The Aboriginal culture is a very old one however it isn't very easy to access. Australians and Aboriginals can be very reserved about the past.
Melbourne is known to be Australia's cultural capital, however, Sydney has plenty to offer. There are many museums that are worth a visit such as the Australian Museum, the Museum of Contempary Art, the Powerhouse Museum and the Maritime Museum.
Each year in January, to fill the lack of activities in summer and draw tourists, the Sydney Festival takes place. With many, very diverse, shows and activities spread over the city for a period of two weeks this is the biggest festival in the Southern hemisphere.
For more information on culture and activities in Sydney visit destinationnsw.com.au.