A good start with lots of promise
I like the original art and the dark humor in this game. The way turn-based combat is handled is also interesting, simple enough to master quickly without detracting from the game's spirit. I also like the almost Diablo-style item placement, but "special" weapons/armors might also be warranted. Though playing with a single character is okay, the fact multiple classes exist begs for a party like some other reviewers are suggesting.
The combat can get a little repetitive but you've done a pretty good job at putting in different combat options. It would be nice to have an "escape" function too, especially since the zombies can be pretty lethal close up. Though in your description you note that zombies walking through walls was intended, it seemed strange to see them burrow through concrete. Maybe you could make slightly more complex terrain rules to eat up squares of movement to approximate climbing through windows or other minor obstacles?
Overall, good game. I'd like to see the next in the series.