Sydney is not a State of Australia, it is the capital city of the State of New South Wales and also the largest city in Australia. Besides NSW, there are five other States and two Territories in Australia: (States) Victoria, Queensland, South Australia, Western Australia and Tasmania and (Territories) Northern Territory and Australian Capital Territory where the Capital of Australia, Canberra, is located.  Australia is a huge country and every State and Territory has its own attractions, advantages and disadvantages. Each State has spectacular scenery and its own diverse environment. Many of the cities in Australia (Sydney, Melbourne and Canberra) have been consistently voted internationally as the world's most liveable cities with gorgeous climate, very high standard of living, high quality housing and surrounded by beautiful national parks. Sydney is one of the most beautiful, vibrant and multicultural cities in the world but also one of the most expensive. Homes in Sydney are becoming exorbitantly expensive and any home within a 20 km range of Sydney brings a price of over $1 Million plus (you can double that price if you have any type of waterview and quadruple it if you have a view of Sydney Harbour)! Also food is expensive.  Melbourne is a fabulous city that is regarded as the "cultural" city with beautiful colonial buildings, world class theatre, fantastic restaurants and lovely leafy suburbs. Melbourne is not as expensive as Sydney but, unfortunately, does not have Sydney's beautiful climate.
I have provided you a link which will provide you with more detailed information about each State and city. You would need to study each city to find the one that suits you. Do not confine yourself to cities, also research some of the beautiful provincial cities and country towns of Australia that offer a wonderful lifestyle which will not cost you a fortune! In NSW, some lovely provincial cities to consider are: Newcastle (on the stunning north coast of NSW surrounded by magnificent beaches and close to the big wine growing area of The Hunter Valley), Wollongong (on the pristine south coast of NSW), Dubbo (a large city about 500 kms west of Sydney which has a lot to offer). Good luck!
Click on the link to give you an overview of each State. Then click on each State of City to provide you with more detailed information on that State ...