I totally agree with the HSBC Premier option. They are actually pretty good. I've been Premier with them for over a decade now and quite pleased. In each country that you are Premier with them, you have to have a certain amount of money with them. In the USA it's been $100,000 US, In Argentina I think I have to have 200,000 pesos but something interesting is I opened my Premier account in Argentina way back in 2003 and the balance certainly has less than 100,000 pesos in it but they still kept me Premier based on all my Premier status in the USA and the UK.
So I think once you make Premier and stay Premier for a few years they aren't so stringent in Argentina. I don't get charged any monthly fees at all. Also, it's nice in Argentina because the locations where they have Premier centers, you don't have to wait in those long bank lines. They typically have a MUCH shorter line. And some centers on a totally different floor so none of the regular customers can see you so there is more privacy.
My Argentina HSBC account is fairly worthless because the banks there are different. But my Premier accounts in the USA and UK are great. I have my own Manager that can help with anything I need. And you can transfer money from HSBC to HSBC accounts with no fee at all or wire to anyone with an HSBC account and they waive the bank wire fee. Plus I can log into my account and see all my HSBC accounts I have (with the exception of Argentina).
If you have the $$$ to open one...it's a pretty darn good account to have as El Expatriado mentioned. But the Argentina account is fairly worthless but I still keep my account there open to pay bills.