The question of whether you need a visa to visit Australia is dictated by the type of passport you carry and the purpose of your visit to Australia; your status as a U.S. green card holder is irrelevant.
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Unless you are an Australian citizen, you will need a valid Australian visa to enter the country. New Zealand passport holders can apply for a visa upon arrival in the country.
Eligibility Requirements for France Visa for Green Card Holders. So, do green card holders need a visa for France? The answer is yes. According to France's entry requirements, any non-European Union citizens who wish to travel to France for more than 90 days must obtain a visa, regardless of their green card status.
Customers must either hold a US visa or a permanent residence card (also known as a green card) valid for at least six months. The 14-day UAE visa on arrival costs AED 120. If needed, the visa can be extended once for an additional 14 days for AED 250.
There is no 'minimum' bank balance that you need to show for an Australian tourist visa. What you need to demonstrate is that you have enough funds to support yourself during your trip. A one week trip staying with your brother is going to cost a lot less that a 6 month trip travelling around all of Australia.
Currently, there are about 38 VISA-FREE countries for US green card holders. A US green card is a pathway to a US passport. While you wait for your US passport, your US green card is already making your current passport strong. Not as strong as a US passport but quite strong.