You should be able to change money in any of the bank branches in King William Street.
The Commonwealth Bank's Foreign Exchange Calculator.
Australia uses plastic money, ie the banknotes are made of a polymer not paper. The Reserve Bank of Australia has more information about the technology and pictures of the current notes.
Nothing really special about them except to note that we no longer have any coins smaller than a 5 cent piece. This means that shops are required to round prices to the nearest multiple of 5 cents, ie 2 cents is rounded down to 0 and 3 cents is rounded up to 5.
Most bank branches should be open from 0930 to 1600 Monday to Thursday and until 1700 on Fridays.
Most ATMs should take foreign bank cards, check for the Cirrus or Plus logos.
Both American Express and Thomas Cook have offices in Grenfell Street where travellers cheques can be changed. Thomas Cook also has a Bureau de Change in Rundle Mall.