From outside of South America, most flights to Argentina are to Buenos Aires Ezeiza airport (EZE). There are also regional South America flights to other cities in Argentina such as Mendoza, Cordoba and Salta with Latam, Avianca and Copa.
There are flights from New York airports JFK and Newark to Buenos Aires with American Airlines, United Airlines and Aerolineas Argentinas. Delta fly from Atlanta to Buenos Aires. American Airlines also have flights from Los Angeles, Dallas and Miami to Buenos Aires. Other airlines which connect Miami and Buenos Aires include Latam and Aerolineas Argentinas. Additionally, United fly from Houston to Buenos Aires. So plenty of choice!
Air Canada flies from Toronto to Buenos Aires with a stop on the way in Santiago.
British Airways and Norwegian fly from London to Buenos Aires. Air France KLM flies between Amsterdam and Paris and Buenos Aires. Lufthansa flies from Frankfurt, Swiss from Zurich and Alitalia from Rome. From Madrid, there are many flights to Buenos Aires including with Iberia, Air Europa and Aerolineas Argentinas. A new route from Madrid to Puerto Iguazu begins in 2019. Budget airline Level flies from Barcelona. Turkish Airlines fly via Sao Paulo to Buenos Aires.
Qatar flies from Doha with a stop Sao Paulo to Buenos Aires. Emirates flies from Dubai with a stop in Rio de Janeiro to Buenos Aires.
Star Alliance members Ethiopian Airlines fly from Addis Ababa with a stop in Sao Paulo to Buenos Aires. From South Africa, a change of planes in Sao Paulo is likely to be your best option.
Air New Zealand flies from Auckland to Buenos Aires. From Australia, you can fly via Santiago or Auckland.
Flying through Europe or the Middle East will be your quickest route between most Asian countries and Argentina.
There is now more competition than there used to be on domestic flights in Argentina with new companies such as Norwegian and Fly Bondi starting to lower fares on the bigger airlines Aerolineas Argentinas and Latam. Often you’ll have to fly via Buenos Aires which has a domestic downtown airport called Aeroparque. Close to travel, domestic flights can get pricey, especially at peak times in Patagonia, so the earlier flights are purchased the better.