Like most places, Sydney has stereotypes for various sectors. The biggies are below, in approximate order of snobbiness. Take with liberal grains of salt ...
The Eastern Suburbs -- south from Bondi, including Randwick, Coogee and the edge of Paddington, among others. La dee da, houses overlooking the water, kids going to private schools, old-ish money.
The Lower North Shore -- just north of the Harbour Bridge, such as Kirribilli, Milson's Point, Neutral Bay, Cremorne, Balmoral and Mosman. Pretty posh, too, plenty of cash, not too many kids.
The Upper North Shore -- north of the Lower North Shore. A bit more inland, good places to raise families.
The Northern Beaches -- from about Manly on up, including North Balgowlah, Dee Why, Long Reef, Narrabeen, Collaroy, Mona Vale, Newport and more. Beachy areas, good for families, a bit more relaxed than the North Shore.
The Inner West -- the chic suburbs, like Newton, Balmain, Glebe and Leichhardt. The residents might not be the wealthiest, but they're cool, artsy places.
The Western Suburbs -- more working class areas. People aren't necessarily commuting in to the city, but going about daily life where they are.
The Shire -- way south, even past Cronulla, which is about an hour out on the train. Still, though, people commute in to the city for work. The stereotypes are the strongest and worst here, but surely there must be some redeeming factor for people called hobbits??
In a category alone is the city -- Darlinghurst, King's Cross, Redfern and Woolloomooloo, among others. They range from sleaze to sophistication and really vary depending where you are. King's Cross is the red light area -- lots of backpackers, but also lots of drugs and bizarre behavior.
There's also some areas south of the Eastern suburbs, but they don't really seem to have a name. For example, Maroubra is a gorgeous beach, but most famous for the 'Bra boys -- a local gang that has claimed the area as their turf, and has quite the reputation for being kings of the sea, surf and sand. They tend toward the violent, and are evidently best left to their own devices.