Been reading quite a few comments about Sydney, and some not very good experiences, so thought I would add my thoughts about the different areas to live in Sydney, and their advantages/disadvantages
In a nutshell, the eastern and northern suburbs are well off, likewise some of the southern suburbs. The further south west you go, the poorer it gets.
The eastern suburbs, so between the CBD and the beach, on the CBD side of the bridge, are the most expensive. Places along the harbour, like Watsons Bay, Vaucluse, Double Bay, Elizabeth Bay, are especially expensive. Veryu nice places to live mind you, if you have the dosh. On the ocean side, Bondi, imho, is a bit overrated for the price, though I have lived there and enjoyed it. Lots of good cafes, a good place to brunch on a Sunday. Bronte, Coogee Beach and Maroubra, the beach suburbs going south of Bondi, are all pretty nice places to live. Something to keep in mind though. The train service terminates at Bondi Junction. So if working in the CBD and wanting to take public transport (the sensible choice, because parking in the city is terrible and expensive), you would get a bus from the beachside suburbs and then the train from Bondi Junction.
The northern suburbs, especial betwen the Pacific Highway and the sea, are pretty nice. On the ocean side, Manly has good transport links (ferry, and buses as a back up in case fog closes down the ferry) but going north, through Dee Why and on up to Palm beach, if you have to commute from there, that means driving, and it is a seriously long haul from there, in the rush hour, to get to the CBD.
Directly north, suburbs like Turramurra and Warringal are expensive but very bush and country style compared to in closer to the city. On a direct line west from Turramurra, about 15 or 20km west, is Castle Hill. Good quality, big houses. Too far from the city for me, but a nice place to live. Beware Lane Cove. Lovely to look at and visit, especially for picnics down by the Lane Cove River, but if you don't fancy a bush fire right next door, don't go there. Some idiot always seems to set fire to it in the fire season.
Going west from the city, the Parramatta Road is a horrible drive if you have to commute to the city each day. If you are living out that way, it's better to catch a train in. Strathfield is very nice, as is Burwood, and close to good schools, private and state.
Coming closer into the city, Dulwich Hill/parts of Canterbury, Lakemba tend to be where a lot of middle eastern families live. The main mosque is in Lakemba. Marrickville is quite Chinese/Vietnamese.
To the south west of the city you have areas like Campbelltown, Liverpool, Cabramatta, and directly west of the city , far beyond Parramatta, you get to Penrith, and then to Emu Plains which is at the foot of the Blue Mountains. These areas have cheap housing, but this is suburbia with a capital S. In summer these areas are seriously hot, as in 40 degrees C, schooling is very so so, - just dull and boring. And far from the sea.
On the south side, Cronulla has a great beach and very good train links into the city. Brighton is nice too. Coming back towards the city, I wouldn't live somewhere like Petersham or Alexandria though - small terrace houses and right underneath the flight path for Sydney airport.
Redfern is not such a good area to live. It has a large population of Aborigines and they can get fairly tanked up on the booze. I wouldn't as a lone woman, get off and walk from Redfern station at night. Likewise from central station. Inner city, they may both be, but not such a good walk to and from the city. They remind me of somewhere like Hulme in Manchester or Muirhouse here in Edinburgh.
Avoid Kings Cross and Darlinghurst. These are inner city but on the east side, and are the red light districts.
If you fancy the inner city on the east side, Paddington is a lovely area to live, though a bit pricey and not really value for money. Just up from Paddington, Woollahra is very nice - lots of good antique shops there. Both have good bus links into the city.
On the inner west side, my favourite part of town is Balmain. Brilliant cafes, good transport links (ferry and bus) to town. Though, if you fancy the ferry, my advice is to live down at the point, near the main terminus, and not on the west side near the Thamse street stop. The west side ferries don't always turn up. Going back towards the city, Rozelle is okay, but not as nice as Balmain - poky houses. Pyrmont and Ultimo are quite grainy. In a way they are trendy, but basically they are converted or redeveloped factories. We lived in Ultimo for a time, and I found the flats were solid but didn't have good air flow. No good parks nearby. Not a very nice walk into town. Going away again, along Parramatta Road, Glebe is a nice place to live. Opposite Sydney University, so well situated if you want to study. Good cafes.
Right in the city, I always fancied living in The Rocks (the area underneath Sydney Harbour Bridge. Good night life but a bit hairy if walking home alone at night.