Matt,
I live (at least nominally) in Sydney's eastern suburbs. I'm a member at St Michael's and - when I'm not living in Sydney (again, only nominally
) - I have some reciprocal rights at NSW, The Australian and Royal Sydney courtesy of my membership of The National.
It's true that NSW is the only must play course in Sydney, but St Mick's is a good intro to sea-side Sydney golf and a nice warm-up before a game next door. I posted a long opinion of Royal Sydney for Chris Kane's benefit on another thread ('Best closing holes on the Sand Belt' or something like that, apropos of nothing) and although it's not world-class, it's worth a game while you're here. But don't waste your time trying to get a game at RS without an introduction.
To round out this complicated membership history, I was for many years also a member at Ran Morrisset's beloved Newcastle, which is definitely worth the two hour drive one weekend if you're going to be here for a few months.
Send me an email (anthony_o'shea@mlc.com.au) when you're down here if you'd like a game at St Mick's on a weekend (it can be tough to get a public time early enough to play 18 holes after daylight saving finishes), or if you want some contact names at The Australian, The Lakes and/or NSW.
Regards,
Anthony.