#1: Capertee Valley and Glen Davis - 2 days here should get you at least 100 species. I can give you more specific info if you PM me. On the way from Sydney while travelling on Bells Line Rd, stop off at Peirce's Pass for an hour - really good birds here usually.
#2: Barren Grounds - you can camp nearby at -34.616151,150.65659 - this area will have a number of species different from Capertee, such as the two specialities Ground Parrot and Eastern Bristlebird, but also Southern Emu Wren, Beautiful Firetail, GangGang Cockatoo, Crescent Honeyeater, Pilotbird, Flame Robin, etc.
#3: Royal National Park - doing a day trip here while staying somewhere in Sydney will get you a lot of birds too - any of the southern wet forest species are possible (gerygones, thornbills, lyrebird, shrike-tit, whistlers, etc, etc, etc). Then heath areas can get you Rockwarbler, Honeyeaters, and more. The 3 sites here are:
a) Southern end of Lady Carrington Drive (park and walk up and back 3kms)
b) Any of the heath trails leading off the main road, such as -34.139834,151.061776
c) Wattle Flat: -34.083188,151.056165 - park and walk south along the small birders trail until it becomes too overgrown. Green Catbird, Shrike Tit, Rose Robin and more are reliable here.
Then if you have time left, there are a number of other good sites to try, maybe look at Warriewood Wetlands, Sydney Olympic Park, Eastlakes Golf Course, a pelagic maybe if there's one on, etc, etc. Make sure to check out
http://www.eremaea.com/ , which is the Australian rare bird reporting service, and also provides species lists for all birding sites. Like I said before, once you've got a plan together, PM me and I can give you specifics!