First, transport is excellent throughout Sydney! I lived in Wooloomooloo, which is (kind of) between Kings Cross and downtown. Later I moved to Darling Harbour. Many young people prefer to live near Bondi Beach, but rental prices tend to reflect this.
Sydney is one of my favourite cities. It's easy to get around however you choose and you certainly won't have any problems, whether it's train, monorail, bus, or ferry!
Long before moving to Sydney we lived up north in Gosford. Transport wasn't as good there and we had to rely on car and rail. But stying in Sydney, you'll have no trouble at all!
I wish you the best
Fr Bill