There are dozens of banks in New York City and for day-to-day personal banking they’re all pretty similar so you should pick one convenient to you. It’s important to consider that if you use an ATM (aka Cash Machine for you Brits) from a competing bank you will likely be charged a service fee of $2 to $4 dollars, so don’t pick a bank that is far away, or every time to you need to take out cash you’ll get charged.
Alternatively, there are some banks in the U.S. that are online only. Because they don't have any physical locations they allow you to use any bank’s ATM and then reimburse you for any service fees.
Note that each bank will have its own policies, such as minimum balance requirements. Make sure you understand any requirements and fees before you open an account.
All bank deposits in the U.S. are backed by the government up to USD $250,000.
WHAT YOU'LL NEED TO OPEN A BANK ACCOUNT
Opening a bank account is a straightforward process. Once you've picked the bank you like you can visit a local branch and meet with a bank rep. You'll need the following documentation:
A social security number (SSN) or individual taxpayer identification number (ITIN) are not required to open a bank account though it will make opening an account with an online-only bank difficult. You can get an ITIN from the United States Internal Revenue Service.
Helpful Money Resources
Building Credit in The United States as an Expat
Tips for expats on foreign currency exchange.