I've played in two games and ran one where zombies were main antagonists and the games lasted more or less for a campaign.

1) I played in a game where my group were all survivors of the rise and recruited by the government (or so we thought) to do regular patrols and missions when the regular soldiers couldn't get there.

2) I played a game in which whatever animated the dead could infect the living and mutate them as well. The ZM gave us dead points that we could use to buy zombie mutations as well as experience. That one turned into a very fun game.

3) I ran a game where colonial marines were fighting an alien force capable of reanimating the dead (a return to my groups Bughunters Roots).

Another suggestion might be to let your players run the market (say on a River Boat) that could lead them into all kinds of trouble.