Howdy flyer.
To give you some answers:
specific sites in Sydney - depends what you like. I wouldn't say there are any real "sell your grandmother to dive there" sites. There are various good pretty easy ocean dives, with a nice mix of macro life (lots of nudibranchs, eels, little shrimp, that sort of thing) and some bigger verterbrates and invertebrates. To give you an example - I did a night dive last night at a place called Shelley Beach in Manly (at the North Head entrance to Sydney harbour). We saw a wobbegong (type of shark), an enormous eagle ray in the shallows, a couple of dozen smaller rays/skates/stingarees, a couple of octopus, couple of cuttlefish, one moray eel, some pretty good size flatheads, and a collection of smaller fish, including a little yellow barracuda that decided to attack my torch! And all that was a max depth of 10m, cruisy dive, no real current, vis about 5-10m, water 17 degrees c. I'd say that's a reasonably typical Sydney dive.
There is a site called Magic Point (boat dive out of Botany Bay, about 10km south of the CBD), which has a cave full of grey nurse sharks - harmless, but properly "sharky" looking, and up to 3m. There's also a few places where you can find weedy sea dragons, which are pretty amazing creatures.
North Bondi isn't the easiest site around. Not hard, but not totally straightforward either. I wouldn't recommend just jumping straight in there with no knowledge of conditions, esp in rental gear. If you do want to do that totally on your own, then I'd head to Camp Cove (inside the harbour, but near the mouth so vis generally decent) - that's a very easy site, shallow, easy nav, hardly any current, potential to see some sea horses.
In terms of timing, the summer is nicer in terms of water temp, but worse in terms of vis. And critter-wise - fewer sharks, but some tropical fish come down instead.
As far as shops go - there are plenty of good ones around: Pro Dive have outfits in Coogee, Manly and Cronulla (bit far out of the CBD), and they're very professional. Frog Dive in Willoughby (just north of the CBD) are a good mob. There's a shop called Plunge Diving at Chowder Bay, inside the harbour, who have a private jetty you can dive right off. It's a hit and miss kinda site - very much muck diving, so you have to be patient and observant. Last time I was there we had a great one though - some beautiful pipefish, quite a few flounder, and most excitingly an anglerfish out for a walk! Abyss diving are also very popular, and have good gear and set up, though I find their DMs to be a bit more full of bravado than I would like - last time I went with them they insisted on picking up sharks left right and center. Not cool IMHO.
I suppose the shop and sites you choose will depend on where you're staying to an extent.
Hope that answers some of your questions. If you've got gear, or wanted to just rent it and not go with a shop, I'd be happy to take you out for some dives. Always like to share the joys of Sydney diving. (Last night's dive was with a bloke just in from California who seemed to like the tour!)
One last thing - you've made a wonderful choice for a holiday. This is truly great city, and a nice place for christmas.
