Ultimo is a suburb on the fringe of the Central Business District, served by both buses and trains (Central Station is a short walk).
It's also near Chinatown, and some theatres and the Entertainment Centre.
I'm not entirely sure about what that income shakes down to be after taxes and health insurance (but it's more than I earn!)
Because of the (reasonably) central location, pretty much all areas of Sydney are available to you.
A 4-bedroom house with pool and some land - the North Shore or Sutherland railway lines, maybe.
Look at Roseville, Lindfield, Killara, up to Hornsby, and then say Hurstville, Como, Sutherland, etc, down south.
Have a look at domain.com.au to give some idea of rentals.
Car commuting to this area is a nightmare, and, unless your husband has parking as part of his package, don't even consider it.
Tax - 45% is about right - I think that's the top rate. All products have a 10% Goods and Services Tax, but this is required to be included in the price of the goods, not added on later, as in some places in US.
Health insurance. I perused
Medibank Private <click>, and the cost of health cover for a family seems to be about $5000/year