Well, if you really like oysters fresh and sunny in Sydney, try two places further up the harbour (but same south side, and accessible by ferry from the main ferry wharf right near the first place I mentioned, or direct by water taxi right out the bar of the Oyster Bar).
The Boathouse on Blackwattle Bay. (I think the address is Ferry Road, Glebe). On the waterfront, great views and service, and a really good seafood restaurant, perhaps the best in Sydney. Upmarket, booking recommended.
Or, the NSW Oyster Growers Cooperative. In the grounds of the Sydney Fish Market, where osyters trucked in overnight from various rivermouths across NSW are sold by the gross (I think it’s actually 20-25 per box, about 15 dollars or so). Shipments up to 5,000 catered for! Grab a box, get them opened, then cross to the harbour side of the carpark and eat. Don’t forget to pick up a bottle of champagne as you wend your way past shoppers and fishmongers.