There's a lot that we don't know about the coming zombie plague and we can't know until the dead actually rise to eat the living. There are a couple things we can say with almost certainty. One is that zombies don't eat brains. The human mouth is too small and the human jaw is not strong enough to bite through a human's skull. We know zombies may prefer brains, but unless they're using some giant nutcracker to crack your skull open, they're not going to be eating any brains. Secondly, zombies don't rise from graves; that's a myth popularized in some movies. Zombies are occupying a human body. They're not based on superstition or myth. They don't have super-human strength. It's easy to test whether or not zombies rise from graves. All you have to do is put yourself in a coffin; bury yourself under 6 feet of dirt and try to get out.
Because you want to stay away from people and populated areas, a cemetery is a very safe place to go if you're stuck outside in a zombie outbreak; often has water, won't be any people there. Even if the bodies in the grave are turning into zombies, they won't be able to get out.