Dead Rising 2 is a zombie apocalypse but is based around one guy stuck in a mall. He is trying to save his daughter by using a medicine which will cure her. He has to fight his way through zombies and humans to try to get this cure.
Fallout: Beginning Vs. End (i only have Fallout 3 and New Vegas, i don't have Fallout 4 yet, but I've heard talk that you get pretty decent armor and weapons right at the beginning... Anyone wish to clarify this?)