Here we are applying zones to your main enemy, the brain craving zombie. As Roger Ma explained in his The Zombie Combat Manual, there is a 'fatal funnel' where the zombies main weapons are focused. That is handy to know but there is more to it than that. You need to be aware of the zombie's peripheral vision and hearing.
Basically, sneaking quietly up behind a zombie and attacking the head is the way to go. Preferably with some long weapon (like a pry bar) that amplifies the impact force and puts some distance between you and the blood splatter. Choosing the right target area and hitting it accurately is vital, otherwise the zombie is just going to get a headache and become very cranky.
Bite off more than you can chew.