Hi there
There's lots of good diving in and around Sydney. I dive a few times a week and there's always something interesting to see, plus it's a lot more colourful than you might expect with beautiful sea fans, sea tulips and the like. My favourite critters are the inquisitive blue gropers, the amazing weedy sea dragons, the three species of cuttlefish (giant, mourning and reaper) and the local shark species including Wobbegongs, Port Jacksons and Grey Nurses.
For shore diving, try Shelly Beach near Manly in Sydney's north, a relaxing easy shore dive in a marine reserve which is usually teeming with fish (maximum depth about 9 metres at high tide). Further south, Gordon's Bay and Camp Cove are also good shore dives.
If you can, try to get on a boat dive. Most dive sites which are accessed by boat are in the 20 metre range (some go to 30m plus), and this is the kind of depth at which you're more likely to see weedy sea dragons. There are a variety of boat dive sites up and down the Sydney coast. Probably the most popular is Magic Point, home of Sydney's main Grey Nurse Shark population. On a good day with good vis, this dive is just amazing, but all of the dive sites have their own charm.
Vis in Sydney is variable, I'd say the average is around 5-10m but it can be worse or significantly better (up to 30m at times) and changes day to day. Similarly, sea conditions change day to day. Current water temperature is around 21 degrees.
I can't recommend a dive shop as I'm affiliated with one of them so Scubaboard rules probably won't let me mention it, but if you Google Sydney boat dives or Sydney shore dives or similar a number of options will come up.
Let me know if you want more information, and enjoy your trip!