Hi WPNinja,
As one of the other people said, much depends on what your purpose would be in obtaining a bank account in the USA. I am in Canada and so I can only tell you my own personal experience, which was attempting to obtain a USA bank account for a Canadian merchant. First of all, I can tell you that obtaining a USA bank account if you do not have a USA SIN has become way harder than it was even 3-4 years ago. There seem to be fewer and fewer banks in the USA that will do this now. We tried all kinds of banks, and finally found a bank that would provide the account - it was U.S. Bank in Seattle. However, we needed a physical location in the USA, USA Tax ID (EIN number), and USA company (LLC). The tax ID is easy to obtain, but the other things cost money so you would want to be sure you found a bank that will provide the account before you spend the money to set up a company and an office rental agreement. There are service providers out there that will set up your company for you, file the annual reports, tell you the cheapest and simplest states to set up your company, etc. There are also service providers that will provide you with a virtual office with a physical address, telephone number and mail/phone forwarding service, for something like $100 per month.