for advertising, if your campus isn't a real jumpy school/campus( i.e. affraid of bomb threats from terrorists wielding nerf guns when your somewhere in ohio...
) i'd cover a big sheet of paper/poster with outlines of people in zombie poses with green(or red if you're daring) paint splattered over the bottom of it with all the info/HUMANS VS. ZOMBIES
in big bold letters. tell em that wont attract some attention!
as for making it seem not so 'childish' do as newbs said and explain who else plays the game,how many people across the world play it, and if that fails try and present it in a formal manner with somewhat of a speech to the dean/principal/WHOEVER is head of fun around there. point out how responsible you can be and take charge as sure not to have anything happen that'd be unsavory for the administration.