Setting up a bank account as soon as possible is obviously a good idea when you move to a new area like Silicon Valley.
There are several major banks here in Silicon Valley : Citibank, HSBC, Washington Mutual, Wells Fargo, and Bank of America. Which one you choose is a personal decision, rather like shopping for a health club - you want the one which gives you the best deal and the best service. You'll be a regular customer once you've joined so it's important that you like the people you deal with and think about close proximity to where you live. Note that Wells Fargo has branches in Safeway and Bank of America has branches in another supermarket chain Lucky. So you may end up choosing your bank where you think you're going to shop. Convenience plays a large part in our lives in Silicon Valley! If you're someone who needs cash or deposits checks on a regular basis, think local ATM machines so you don't end up paying charges for using another bank's ATM.
You can also set up your credit card account at the bank, though if you're coming into Silicon Valley from another country, you may have to wait three months until they know you are creditworthy and have a regular income before they'll let you have a card.
And credit-worthiness is important, so get one as soon as you can, especially if you're looking to take out a mortgage in the near future.