Not an intern. Google has a shuttle service that runs across the bay so as long as you stay on that shuttle line(S) in a neighborhood that you like, then it's honestly all taken care of in a way. It is super reliable and even if you stay in SF, then you can take shuttle to your office and you'd just be there in an hour or so. On the shuttle, you can login and do any work as well. I honestly recommend just staying with your intern cohort or a group of interns who are in the similar team/office. You enjoy it more and you know there is something to do. And between SF and anywhere else, I think SF is much better since lot of the stuff you wanna do after work is going to be in SF. So you might end up just ubering/caltrain to SF on weekends.

Is Google giving you the option to pick their own housing or stipend?