Australia Option 1: There are typically 4 flights per month (As of March 2015) from Travis AFB through Hickam, Hawaii and sometimes Andersen, Guam to RAAF Base Richmond (near Sydney). Occasionally, flights return to the US from Richmond via Christchurch, NZ. Normally, these flights have few seats available, so while possible, it is difficult to get on the run to Richmond; however, returning from Richmond to the USA is often easier.
Australia Option 2: Space-A to Yokota and then Space-A to Singapore (3 weekly) and then use commercial air from Singapore to Darwin (about $100 or less one way) or Perth (about $200 one way).
Australia Option 3: Space-A to Hawaii and then check fares on JETSTAR Airlines from Honolulu to Sydney (just under $400 one way).
NOTE: All foreigners entering Australia are required to obtain visas Australia Electronic Travel Authority (ETA). In addition, upon leaving Australia you must pay $55 AUD cash (as of March 2015) to its Customs and Border agents.
New Zealand: Space-A to Hawaii and then try for a "rare" mission to Christchurch or try commercial from Australia.