Not surprisingly, the best deals to Argentina are offered by Aerolíneas Argentinas and Lan-Chile in conjunction with Qantas and Air New Zealand, either direct to Buenos Aires or via a stopover in Santiago. To get to other destinations in Argentina, such as Río Gallegos, Ushuaia and El Calafate, you're looking at either an add-on fare or air pass from either of these two cities. There are also plenty of flights via the USA, but only United Airlines is scheduled through to Buenos Aires - other airlines tend to offer much more time-consuming and expensive routings, as each sector has to be costed separately. Round-the-World tickets that include Buenos Aires, and Circle America fares, are also quite expensive, but can be worthwhile if you have the time to make the most of a few stopovers.
In Australia , most flights to Argentina leave from Sydney, though there's also a couple a week out of Brisbane and Melbourne. The most direct route to Buenos Aires is shared between Aerolíneas Argentinas and Qantas via Auckland while Air New Zealand/Lan-Chile's routings are a little more long-winded, flying via Auckland, Papeete, Easter Island and Santiago (as flying time is around twenty hours you may want to take advantage of the one free stopover allowed each way). From New Zealand , as from Australia, your best bet is with Qantas, Aerolíneas Argentinas or Air New Zealand/Lan-Chile. You can also travel via the US with United Airlines, who fly to Buenos Aires from Sydney and Auckland via either Los Angeles or San Francisco, and Miami.
If you plan to do a fair amount of travelling within Argentina (or to other South American countries), think about buying an air pass with your main ticket. These passes offer substantial savings, but can be bought only outside South America with your international ticket.
