It looks like about $1400 one way for an inside cabin, so about $3000 round trip.
A quick perusal of Sydney cruises brought up destinations of: Seattle, Honolulu, Los Angeles, Vancouver, Singapore and Hong Kong. All running anywhere from 2 to 4 weeks.
Looking on the Cunard website, for advance booking of balcony cabins on winter 2016/17 transatlantic sailings, it can go as low as £1049 per person each way, so say $3000 for a round trip. Ocean view and inside cabins are cheaper. You can play about with options here:
You can travel as a passenger on freighters on at least most of those routes. For example, CMA-CGM’s Pearl River Express has weekly sailings from Oakland, California, to Hong Kong and several Chinese ports, returning via Long Beach. Of course, these ships carry a maximum of ten passengers and the full roundtrip takes a month and a half.
And as far as I know, these freight ship passages are actually the cheapest options that are available to those who absolutely insist on travelling by ship. What you get is a no-frills spare cabin, you are served the same food as the crew members and there is absolutely no onboard entertainment (other than, maybe, a DVD player).
In 1972, my family traveled from Los Angeles to Taipei, Taiwan, on the President Wilson (American President Line (APL)). That was our last oceanic trip by ship. (At the time, it was cheaper to take an ocean liner back and forth from Taiwan to the USA than it was to fly. Plus, we got a nice 2-week vacation out of it!)
According to Wikipedia, the President Wilson was the last passenger ship of the APL and was sold off in 1973.