In reply to HarmM: Hi Max,
I also lived and climbed in Sydney for a good few years. I pretty much found a car essential, however if you get down to the St Peters Climbing gym and seek some advice I am sure public transport or lifts are easy options.
There are a few half decent sports crags on the north shore of the city, Mt Kuringai being one and Berowra another. If you get the chance Barrenjoey head is great too. Climbs are not amazing but there is a mix of sport and trad and its on a tiny spit surrounded by the sea and some great beaches to cool down in after a good climb.
A few hours south of Sydney there is a place called nowra which is full of sport climbing up to about 30m loads of crags and a good range of grades from easy to really hard - A bit far for a day trip but weekend with camping on the river was the way we used to do it.
As Alan mentioned Blue mountains is good and has load to offer with some really great multi pitch - I particularly liked, Mt Piddington.
You have to get to Mt Arapilies too.
Hope that helps