The bigger concern would be other survivors. zombies are bad but they don't lie, cheat, steal, or try to kill you for the supplies you have that they do not.
Avoiding populated areas would be the priority. After that, it's a numbers game- there are more of them.
So staying mobile would be preferred over trying to fortify and fixed position. Supplies will run out and trying
to make a food run through the horde that has gathered around the building only to have to fight your
way back in?.. not a good position to be in.
maintaining temporary camps that can be secured for the short term and abandoned quickly before
making a significant impact would be the way I would go. Doing so would allow sustainment through hunting and foraging
without exhausting those resources, and make it possible to stay ahead of the corpse march that would inevitably being following it's food, once the cities were exhausted.

you can see how these basic life saving steps were not followed in the documentary "Dawn of the Dead". and we all know how that turned out.