As a tourist in San Francisco, can I simply walk into a bank and open an account?

You can. Surprisingly, many people think opening a bank account as a visiting tourist (foreigner) you will run into problems. That is not the case. Some banks will require an address, you can use the hotel's address if you wish, and then request the bank to put a hold on all mails and statements.

All you need is your passport and (perhaps) a secondary form of ID. A little cash to open the bank account with. Its relatively a very easy process.

What can put a damper on the whole experience is if you come face to face with a bank representative for new accounts, who is oblivious to the laws and how foreigners are allowed to open bank accounts in the US. Talk to the manager if necessary. You can cite, that you have just moved or are in the process of just moving to the US, and the address is really not an issue.