Whotto mate:
I did 5 weeks riding in Oz last year but had the benefit of a friend who lived over there and he organised a big road trip.
In Sydney there's only really the marked route at Manly Dam. Quite a nice route with a couple of techy bits. I was told that it suffers in the rain but I was lucky while I was over there as it only rained the day I was wandering around the zoo.
http://nobmob.com/rides/manlydam
From Sydney's city district you need to take the ferry to get to Manly. It's no stress with a bike and pretty cheap too. You also get fantastic views of the bridge and the opera house – saves spending out on the tourist boats which take the same route.
You could also take the train out to the Blue Mountains where I did a couple of nice rides.
I took the train to Katooma and did this ride to start:
http://www.users.on.net/~fathers/narrneck.htm
It's an out and back with fantastic views and the odd short, steep climb but mainly fireroad.
I then hopped back on the train returning to Sydney, stopped off at Woodford and did this ride:
http://www.users.on.net/~fathers/sthelena.htm
Really nice ride with lots of singletrack and a bit of get off and walk as the flying doctor can't reach you there. Basically drops you off at the next railway station along to Sydney so you hop on the train back to Sydney and job's a good un. We did both on the same day by starting out fairly early. Again bikes on train are stress free and pretty cheap.
Worth noting that with the rides in the Blue Mountains you really don't want to be taking a wrong turn.
To be honest though, the best riding both quality and quantity wise was in Canberra by far.
Notice from your profile that you're South East London based. I've got some mtbing mates based in Bexley but I'm in NE London, right on top of Epping Forest.
Let me know if you need any more info.
Cheers,
Mark