Hi Jane.. I was originally from the UK nearly 60 years ago ( I'm pretty old ) You will find us Aussie's pretty funny sort of people, don't have a great regard for authority of any kind...unless you earn it first. Sydney is in New South Wales, Melbourne is in Victoria... Victoria is where the rest of the Australian states send their sh@t weather. Sydney has the biggest coat hanger in the world and the biggest oyster shells in the world stacked next to it. It's a great place and I have many great friends there ( also a lot of relations and friends in Melb as well, who are great and I feel very sorry for them having to live there

).
Sydney has top class restaurants and fabulous beaches, it's a very very busy place to live.. Cheapest accommodation is in the suburbs, a flat , depending where... Would be in the range of $250 up per week, share accommodation is the cheapest way to go. Can't help you with air fares etc.
If you have any trouble with getting a job in nursing, ( which I doubt ) up here on the Gold Coast in Queensland, they are desperately short of nurses and I feel sure if you were to contact a hospital here, they would more than likely, be able to help you out as far as accommodation is concerned as well.. The gold Coast is of course, the best place in Aussie to work and live, we have the best sub tropical weather, we are very, very friendly. Have over 500 top restaurants, a population of half a million permanents and floating one of a quarter of a million tourists, heap of good night clubs ( so my grand children tell me ) absolutely, the best beaches in Aussie... And I'm not bias in any way

. If you want any other info just ask.