As well as whatever Aspers advises, get hold of the Lonely Planet Guide.
Have a coffee in David Campese's cafe down the Harbour.
Be careful where you change your money, and it's a crap exchange rate anyway.
Have a look at
http://www.Tripadvisor.com/Sydney.
Have a look at the Thorntree Forum on Lonely Planet.
Visit the Blue Mountains (easy day trip) by train, and well worth the effort.
Have a meal at the Fish Market.
Take a ferry or three from the Harbour.
Go to Melbourne. It's cheaper, and that's where Ned Kelly came from.
Chinatown is in Bangkok!
Don't say to an Aussie, "What do call an intelligent Australian?", or "Any idea what the west island of NZ is called?"
Ask you aircraft pilot to do a couple of loops over Sydney Harbour, it's cheaper than climbing the Bridge.
I'll get the scrapbooks out, and come back with more