You got your standard landmarks (that big bridge, that big rock, that big tower, that big opera house, that big banana, etc), melbourne's multi-culturally influenced areas, the beaches on the east/west coast, giant fireworks in Sydney on New Years, giant fireworks in Brisbane in September, or you could experience Christmas in 40 degrees Celsius heat!
Darling harbour has the harbour bridge and operah house. Could also take a ferry to manly and toronga Zoo. Toronga Zoo overlooks darling harbour. We also have some pretty nice beaches.
We have a big red rock in the middle of the country. Because ive lived here my whole life I don't really know what foreigners find appealing about here. New Zealand 3 hours flight from east coast is a very nice country to visit if your into nature and scenery