Aliens can only stay on a tourist visa in the United States for a maximum period of up to 180 days or 6 months. Note that: In some cases, the United States Customs and Border Protection (CBP) officer will establish a specific time of stay in the country, so it can be a period shorter than 6 months.
You must have a valid U.S. passport and a visa or an approved Electronic Travel Authority (ETA) to enter Australia. Most U.S. passport holders traveling to Australia for tourism or business purposes for less than 90 days can obtain an ETA.