Hi Joe,
There's quite a few to choose from but here's a start -
cyclery.com.aucyclery.com.auOpen ↗ (Sydney City: three levels including workshop, plenty of stuff to choose from, a little pricey)
fraserscycles.com.aufraserscycles.com.auOpen ↗ (south of Rockdale; about 20-25 minutes drive depending on traffic, large store, good prices, nice staff)
woolyswheels.comhome.htmlOpen ↗ (Eastern suburbs; not far from the city though, very good range, prices are what you expect for a store near the city)
citybikedepot.com.aucitybikedepot.com.auOpen ↗ (reasonably new store compared to the others, very nice people to deal with, good range, I recommend them but am biased as they are just down the road from my work and I like to drool over their bikes)
phantomcycles.com.auhome.phpOpen ↗ (an hours drive or so out of the city but these guys have great prices, great service and a great range. From Rockdale it shouldn't be too hard to get to as the M5 freeway is not far and it's a pretty straight drive from there.
I figure if you're after a full suss you'll be doing some off-road riding while you're here so here's some links to get you started -
members.iinet.net.aumtb.htmOpen ↗ (very good ride descriptions for the Blue Mountains area)
nobmob.comnobmob.comOpen ↗ (descriptions and pictures of rides on the northern beaches/north shore area and a few others in and around Sydney)
shutupandride.netshutupandride.netOpen ↗ (apparently a psychotic, but nice, bunch of mountain bikers)
members.ozemail.com.auSydneyrides.htmlOpen ↗ (pictures and descriptions of some rides around Sydney)
Enjoy your stay 🙂