If you are working in the CBD there are many surranding places you could live. It really depends on what you are interested in and how you prefer to live.
You could pick the inner west which has a more trendy vibe to it, the North Shore which has a more relaxed feeling or if you want the beaches you could try Bondi area, or even Manly if you don;t mind relying on the ferry to get to the city.
It is nto too common to get furnished places in Sydney, they can be found but its harder. If your only staying for a year or so and don't mind "not so great furniture" you could try Fantisatic Furniture for cheap start up furniture.
All appartments come with an oven/washing machine and some a dishwasher. If the appartment block does not have an area outside for you to dry you clothe son they have to by law provide a dryer.
Pets are fine in most places although you have to get permission from the Stata.
Try
www.domain.com.au or
www.realestate.com.au for rental properties!
Hope that helps
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