Hi there
I live in Sydney so feel well qualified to help you out with any questions about my fair city!
The cost of living in Sydney is about 75% the cost of living in London- I know as I've been there recently and been grocery shopping with my best friend, who lives there, and was astonished at the prices you guys pay for food!!
As far as rent goes, this varies enormously depending on which suburb you want to live in. Give me some more details and I'll be happy to supply some median rents for you here.
As far as AUS $100K salary goes, this is quite high and well above the national average of $49K. How much you spend naturally depends on your lifestyle habits, however

For income tax rates see this link:
Individual income tax rates
As far as air con goes, this again depends on where you live, how much rent you're willing to pay, and whether or not you need it to survive. We only just had ducted air installed last year, and it is well used in our summers. However, there are loads of properties with air con so you need not be worried that we don't possess such luxuries! By the way, our heating/cooling costs are also a LOT cheaper than what UK residents pay.
The best rental sites for Oz are
www.domain.com.au and
Real Estate, Property, Land and Homes for Sale, lease and rent - realestate.com.au - you will be able to get an idea of what you should be paying from looking up these. Any other questions- feel free to ask!