Caution:
As a foreigner you may have a problem joining a credit union unless you have a green card. I know a few of credit unions that have these kinds of restrictions.
I say go to those that know how to deal with foreigners. (The last thing that you want is to have your account locked out because a small bank/credit union did not know what to do with you, opened an account and it was flagged down the line - maybe 6 months later).
Those would be:
1) Big national banks
2) Big international banks such as HSBC
3) If you are by Chinatown, look for banks servicing Asian population
After you open one account open a second account in a different bank. You do not want to keep all your eggs in one basket, especially as a non permanent resident. Dealing with an account lock out is especially annoying without a network in a country.