The Tully is class 4 boulder garden. It's pretty fun, everything is easily portagable as there is a path around everything (and there are big pools to collect any pieces) :-). It's hydro release, so water is regular. The Barron is Class 3, and very straight forward.
Sydney is a little bit more complicated. Glenbrook creek runs occasionally, class 4 creek, but watch for the trees..., Penrith is regular (they call it class 3, but really it's probably class 2 - man made). Pretty fun though. There's also stuff further south in the Snowys.
Between Sydney and Brisbane though,t here is some awesome stuff. The Nymbo is class 4 pool drop, and a fantastic part of the world to paddle in. There's plenty of stuff around there around the Dorrigo plateau - the Little murray, the Gwydir ... Goolang (class 2 but fantastic camping).
The main regular water rivers would be Penrith, Tully and the Nymbo. The others are sporadic.
re Grading... I've never paddled in the US, however I have paddled in Canada (BC and Alberta). My experience is that the grading in Australia and NZ was significantly harder than that in Canada. Most of our rivers are quite remote (ignore this for the Tully, Barron and Penrith where there are plenty of people), and your mobile phone will not work in most of these places. You will be usually at least a couple of hours from help (usually more). I'm not trying to be alarmist, but please make sure that if you get on some of our fantastic rivers you go prepared to get yourself out...
Bring your own boat and gear, as hiring is difficult (especially if you want nice gear).
Hope this helps... give me a yell if I can help further