Hi mad_atta,
You went from Sydney to US at this point? In the middle of one of the worst US winter every vs Australian summer? You got a bumm deal and should have requested a delay transfer after the summer
Seriously, it is a bit painful to get an US credit card after relocation or partial relocation. I have friends who relocated from France and they were using their corporate AMEX even for personal expenses (removing it from their expense reports) and found out after 1 year that they still don't have any credit history and it was tough for them to get a card.
Since you have the HSBC Premier, and you want to establish credit history ASAP, I would suggest you open 1-2 department store card such as Macy's, etc.. I opened a Marshall Fields one (2 years ago before it was converted to Macy's) based on my Canadian passport and Canadian credit cards and had $1000 or $1500 credit very easily and 10% shopping discount for 2 days... Saved me an extra 80-100$ plus sales tax so closer to $150 savings.
Macy's is a bit more uptight but if you have the HSBC premier with a few months history, they should be able to give you one, even if it is small credit limit. You want to pay them on time or early for a few month and it should help with your HSBC Premier to get more cards.
If you travel a lot for business/pleasure, the SPG AMEX is worth looking into since it can have a lot of bonuses...