I was going to run a zombie apocolypse as my next roleplaying game, but I was going to keep the theme a secret and have the players make modern NORMAL characters and THEN spring the zombies on them.
The only problem is that the zombie apocolypse is a one shot game, not much fun roleplaying a character hiding in a bunker who can't leave.
Sure you can, you add an NPC (or NPCs) who falls into one of the major ZHM (Zombie horror movie) stereotypes.
-The over-protective spouse/parent who refuses to see that their loved one is doomed to become a zombie, lashing out at whoever tries to kill/dispose of the budding zombie in their midst
-The greedy individual who sees some form of profit in the whole situation
-The stir-crazy lunatic who sees zombies as a form of salvation or redemption, or who feels it is too hopeless and wants to end it all for the whole party
It just becomes a far more psychological game, especially as food & supplies run out, radio contact with others dies off, repair supplies begin to prove inadequate to hold off the ravening hordes. Yeah, you can't run a hack-n-slash zombie campaign, but a story-driven campaign is very possible, there's jsut less dice rolling.
As for where I'd go? Cruise ship, if possible. Lots of supplies, water desalination facilities, plants (so there's some possibility of raising crops), plenty of escape means, controllable access points (gangplanks) so even if it never left dock it's defendable, generators, high power radios, helicopter landing strip. And enough supplies to create a zombie killing field/chamber. The only way to eventually stem the tide and restore balance is to be able to lure and kill large numbers of zombies in a safe, repeatable manner. Yes, given the numbers of zombies you're dealing with, you'll likely never reach that point before you're dead, but at least you're making some small progress.