Applying for Australian Visa within the US for a non-US citizen.

Don't know where else to ask this, called the Australian embassy in the US and they didn't know much more than I do.

I'm planning to apply for a tourist visa from within the US, the problem is that I'm only a US resident and not a citizen and therefore cannot apply for an ETA. I hold a Thai passport and a US green card, what would be the easiest way to go about applying for an Australian visa? Where do I take my biometrics? Any Application Support Center near me?

I really don't want to have to travel back to Thailand just to apply for a visa so any help would be greatly appreciated!