Crowbar is one of the best weapons you can use for close combat against a zombie. It doesn't run out of ammo, it's solid and able to crack a skull, it's light enough to wield one handed without getting tired fast, and you can use it when escaping to pry open doors.
Now, if we're gonna talk about zombies they've gotta be the slow zombies because the master of the zombie movie George A Romero himself has said and I quote "fast zombies suck". And since they'll be Romero's zombies, you have to realize that anyone who died became a zombie, not just those who were bitten. The bite just eventually killed you.
As far as where to go, Alaska into the arctic. Already not alot of people there, so the initial zombie population should be low. And then you've gotta consider what happens to zombies in the cold. A corpse has no body heat, so eventually the zombie bodies would freeze and be unable to move. True living in Alaska isn't much of a life, but if you get a decent stock pile of fuel you can stay warm and power generators that probably already exist in the houses. Now just make sure that you bring at least 2 or 3 HOT girls with you, and you can live out your life being the last man on Earth they'll ever see.