In Sydney how about getting off the road and trying the cycle paths at the Bicentennial Park (at the Sydney Olympic Park where the Olymipcs were held) I haven't done this yet but it look ok

http://www.sydneyolympicpark.com.au/...cling_circuits

you can hire bikes out there too, I think the website shows how to get there, you can even catch a ferry.

http://www.sydneyolympicpark.com.au/...ike_hire_@_sop

Centennial Park (different and closer to the city) is the home of cycling in Sydney and many clubs ride there - I'm sure you would find serious cyclist doing sessions every morning and night of the week and more so on the weekends.

http://www.cp.nsw.gov.au/visitor_inf...ies/sub_page_3

Light_sabre is right, the roads (and drivers) in Sydney are pretty cyclist unfriendly. There are good spots to ride but you really have to know where to go and be familiar with the place. There is a good book that was produced for Sydney cyclists and commuters though called "Bike It" which was produced by a guy (Bruce Ashley) that must have ridden every street in sydney.