Stanford campus is, I would say, hostile to cars. Stanford is a very big place as far as university campuses go and besides a loop road around the edges there are only a few roads that go to the inside and a lot of it you simply can't get to by car. You need to park and walk or bike. If you do choose to walk, don't let your guard down because while the cars are absent, the bikes are still a (slightly less lethal) menace.