Trout may be the romantic notion of freshwater fly fishing, but lots of other species are available, and many in the Sydney basin. Australian bass, a river species which travels to the salt water for breeding is an iconic fly fishing target. A powerfully designed predator, they strike a surface fly with a voracity which is hard to compare.
The Nepean/Hawkesbury River system, the Colo River, in fact most of the major rivers which connect to the sea will hold bass. Cast flies around structure, under overhangs and under trees.
In summer, the bass will lie patiently watching the surface for cicadas and other insects to fall in, then strike violently. Surface flies such as the Chenobyl Ant and gurgler, and subsurface flies like the vampire are effective summer bass lures. Casting towards the shore from a boat is preferable, but these aggressive creatures will be in the deeper water too.
Carp, whilst considered a pest in Australia, is none-the-less a great sport fish and a wily adversary for any fly fisher. They will take surface flies similar to bass, subsurface flies like the woolly bugger (emulates small fish or leeches), bread flies and corn flies. As all states of Australia request that carp be destroyed, there is no closed season and no bag limit. Using burley to attract carp before commencing fishing is acceptable practice. Always remove carp from the river bank.
Herring can be found in the fresh water network of Sydney. Surface flies like the muddler minnow will attract them.
In general, fresh water fishing in Sydney is a not a very specific sport. The same fly that targets a bass can catch a herring and carp will eat almost anything. The warmer months are usually more productive as most of these fish are either dormant in winter or swim out to sea to breed.