Some excellent ideas in this thread, thanks all.
I'm veering towards making it a regional thing, and not only zombies but a variety of undead. I'm thinking the PCs would start out in a small town and hear about "walking dead" in nearby farms, with calls for people to help out. It will soon get out of hand, with a veritable horde of zombies on the prowl. Hopefully the PCs will become interested in the cause of this, and as they explore they start encountering more powerful undead, that the lesser undead are actually being led and controlled. They start hearing of a Grey King, who they find is the undead former ruler of an elvish kingdom that was destroyed, partially due to human expansion
This sounds like a hack & slay adventure.
Why are the undeads attacking? What does the leader want?
Why does the Grey King rise this days and not earlier?
What happens when the PCs just head elsewere and ignore the quest?
Give them an interest to fight the undeads.... maybe they surprised the PCs on resting and one of them got infected, slowly turning to undead. Do they want a cure for their companion?
Build in some twists in your story!

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.