Hey man,
I've been living in Sydney for the last 5 years and honestly... there's nothing worth buying here if you ask me. Not even strings. Everything is, dollar for dollar, more expensive, and once you add in the lousy exchange rate now, I wouldn't even buy a pick here. Still, if you *must* go to a guitar shop, you can try the following
For new guitars,
Venue Music and Allan's Music, both in the city. Venue is behind Queen Victoria Building, and Allan's Music is along Pitt St. You can also try Billy Hyde's near Pyrmont Bridge Road.
For second hand stuff, try Guitar Crazy at Coogee or Jackson's Rare Guitars, which is near Leichardt I think.
For the addresses, Google is your friend