PhilD has it spot on - people are drawn to restaurants that suit their style and taste.
Sydney people choose restaurants also based on "its the scene". that said we are very relaxed and no one will say anything unless you really go out of your way to dress down.
Agree with Onara. Definitely Quay.
Sydney has very interesting small bars which do great food. Bootleg in Darlinghurst.
Gastro park in Darlinghurst is a must do - its very playful and the cut above the rest.
Berta in Darlinghurst I would suggest is very Sydney in its attitude to food in terms of cooking and use of produce.
Surry Hills/Darlinghurst has a huge array of restaurants so you really can't go wrong. Check out Sydney Morning Herald "good living" guide (food section in the paper) it gives regular reviews and tips of the latest and greatest in Sydney.
Also for lunch try the pork and fennell sausage roll at Bourke Street Bakery. Very Aussie with a twist - can't say you've been to Australia without trying a pie or sausage roll!! :)
Definitely Hunuman (have the oysters its the house specialty) and the beef rendang.
Parap markets on Saturday is brilliant. There's a lady there that makes the best paypaya salad I've had.
Mindil Beach markets are amazing - although I've never tried the "road kill" food stand for some strange reason...