Darren,

While I don't have personal experience with a guide in Sydney, this
information may be helpful.
In "Where to Watch Birds in Australasia and Oceana" and "The Complete
Guide to Finding the Finding of Birds of Australia", they mention the
Royal Botanical Gardens is near the city center. It has a good variety
of species, including Tawny Frogmouth, Superb Fairywren and Eastern
Spinebill. For a short trip out of town, the Royal National Park is 40
Km south of Sydney, it has a variety of habitats and site list of over
200 species.
The Birding Pal website has two individuals listed in Sydney.
http://birdingpal.org/Australianew.htm
Birding Pal is a service where local birders volunteer to show you
around or offer advice, in the hopes that you will reciprocate when they
travel to your area.
A quick web search picked up at least one tour company that runs birding
tours in Sydney for about $125/day, minimum two people
http://www.birdingtours.com.au/
You could also contact birding guides from other areas and see who they
recommend. We went out with Philip Maher in Deniliquin and Klaus
Uhlenhut in Queensland, they would be good places to start.
It will be difficult not to have a good time on your trip!

Best of luck,

Jack Stephens
jstephens62 at comcast.net
Edmonds, WA