I am flying Bangkok to Christchurch, NZ. I have a 6 hour layover in Sydney so I have a visa to go out and explore for an hour or two. Both flights are Qantas so I don't need to check my luggage out.
Sydney airport varies, if you're fast (run!) to immigration, you can get through pretty fast if no other flights are arriving at the same time.
From there, it's a train ride to the city. Takes about 25-30 minutes to Circular Quay (where the Opera House etc is).
Coming back, for a flight to Christchurch you have to be checked in at the latest 90 minutes before hand (source: I flew from Sydney to Christchurch last night, and do it often). However there's sometimes a queue, so aim for 2 hours to give yourself a buffer.
Getting through immigration to exit Australia is pretty fast, it's the security area last night that took me about 20 minutes - bit of a line at the x-ray machine. After that it's 5-15 minutes to your gate. I was at Gate 60, probably the furthest from security.
If you can, check in online for your flight, that'll save you time when you're back at the airport.
As an aside, in Christchurch run as well. 3 planes arrived last night at the same time, and while passport and baggage were quick, the customs line took a good while...
