Hey, my 2 cents worth.
So we went to BofA adnd open a checking a/c - UK address, US mailing, no S.S., but passport. They charge $5 p.m., but they have a scheme whereby the charge is waived if we opt not to use teller services (don't ask). Comes with checks, ATM debit card and online banking. Uses a pin number for gas stations. The bank A/C can be paid into using ATM (of course you have to be in the country for that) or Paypal.
They biggest problem with U.S. money is using our UK Credit card online to buy in America, as they inevitably ask for a zip code for the card, of course we don't have one, but the debit card has the mailing address zip code, which makes everyone happy.
Just hope this solution holds together till the next terrorist/banking crisis.
Another solution:
We have also made wider use of cash cards. Buy a $ currency card in your home country, you can top it up online. Look for a card with a good rate of exchange (I mean the % they take for changing the money, some cards are as little as 1% off the true exchange rate, some can be 3 or 4%), and also zero charges for using an ATM.
To buy a cash card in the U.S. is not as easy, requiring an S.S. number (if I remember rightly). Though of course you can buy 'gift cards' at places like Walmart, which again you can top up.
Of course you could just give me your money and I will bring it into the U.S. and spend it for you as well.