Sydney is most often broken up into the following suburbs: Eastern Suburbs, Hills District, Inner West, Lower North Shore, Northern Beaches, North Shore, Southern Sydney, South-eastern Sydney, South-western Sydney, Sutherland Shire and Western Sydney. The City of Sydney is keen to promote Sydney as being a city comprised of villages; therefore, different areas are sold as having different characteristics and feel.
Sydney has generally good public transport in well established areas closer to the city, so it's easy to get around the inner areas. However, road signage can be lacking, so navigating can be tricky.
Culture vultures are well served with the opera house and a collection of theatres. There's also lots of emphasis on sport, with rugby league dominating but union, football(aka soccer) and Aussie rules also get a look in. Sydney is also home to the SCG which is one of the world's loveliest cricket arenas - there is usually a Test match starting there early each New Year.
Sydney also enjoys its reputation as a liberal, alternative place with the Gay and Lesbian Mardi Gras festival as the showcase (annually in Feb/March). There are lots of more mainstream festivals, many free and aimed specifically at families.
It's not a cheap place to be, ranking as 19th on the list of world's most expensive cities to live in 2006 (Mercer). Accommodation and entertainment costs are high (and on the increase), as are utilities, transport, and drink. Sydney does not compare favourably against other places in Australia. Buying your own house is probably the biggest expense with house prices more expensive than London and New York as a multiple of income. Rent is cheap but currently on the rise. Cheap places can be found in the south west and mountains but public transport is scarce and commute times to other areas are horrendous.
But it's got a laid-back feel, is easy on the eye and the harbour makes you smile most days. Just close your eyes on the drive through the west on the way to the mountains.
There's lots of information about Sydney on the net. A good place to start is: http://www.cityofsydney.nsw.gov.au/AboutSydney/Default.asp
A good website for a summary of Sydney Suburbs is: http://www.cityhobo.com/