Are a business or as an individual? As an individual, I always prefer a credit union which is like a not-for-profit bank. With a sufficient amount in your account, you shouldn't have to pay monthly fees. Credit unions tend to have lower fees than the big banks in general.
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.
Thanks for that. I'm still waiting for my physical green card; apparently it can take up to 3 months for it to arrive. But SSN takes just a few weeks apparently.
Good tip about Chinatown. I don't live that close, but don't mind going there to open an account.
I use TechCU which is more prominent in south bay. I've had good experience with them for decades. They should be able to deal with recent immigrants given that they deal with the tech community. However they have just one office in San Francisco. But do shop around as you can get great deals (like $200-$300 bonus) for new members with direct deposit of your paycheck.
SF Fire Credit Union has free accounts, and is open to anyone living or working in SF. They have great service, refund atm fees from other banks, and don't charge foreign transaction fees.