Nuclear war, zombie outbreaks, meteor strikes, economic collapse, alien invasion, no matter how it happens an apocalypse makes for a unique and engaging setting to run a campaign in, even for a jaded GM.
Here’s a few quick tips that can make a good zombie or other post apocalypse game a great one, and keep the group coming back (from the dead?) for more.
The PCs accidently start a fire and are caught by the local law enforcement. Since it was accidental, the punishment for the PCs is to fight the fire. Providing they can put it out before it burns down the town, they will not face any further punishment.