Ok, firstly - Sidney? Really? Wikipedia lists one of those in Canada, and a bunch in the US. And of course Sidney Sussex College at Cambridge University - a fine institution at which I spent my undergraduate days.
Perhaps you mean Sydney, the largest city in Australia?
Next, is Sydney near the Great Barrier Reef? Hmmm.... would you think asking if New York is far from the Caribbean, or Novo Scotia far from the Rockies a stupid question? Mate, I've got to tell you, 30 seconds of google searching would have answered your question.
But whatever, I'll answer anyway. No. It's not. The Great Barrier Reef is only on the north-east of Australia. The southern tip of it is more than 1000km (so 700+ miles for those who prefer their measurement systems illogical) north of Sydney. If you want to dive there, fly to Cairns or Port Douglas, then go out on a boat, either day tripping or better still liveaboard.
Don't let the absence of the GBR in Sydney put you off diving here though. There is some excellent diving right in and around the city. You can see colonies of grey nurse sharks (up to about 3m in length and scary looking, but totally placid), huge gatherings of sea horses, lots of colourful nudibranchs, and even the incredibly charismatic weedy sea dragons. And all your usual eels, octopus, cuttlefish, and lots of pretty and interesting fish, and other vertebrates and inverterbrates. Shore dives or boat dives, both are easily done.
