Not bad
It seems a bit ridiculous for survivors to simply run off. I'm just saying.
An idea I had, if you're feeling rambunctious, is to have your character popping up in different houses or shacks as they make their way to safety. Of course, you'd probably have to drop the price for defense bonuses, as they wouldn't last when you change buildings.
Another idea to add would be a difficulty option which would dictate what you start with.
If you want to go with that 'side view' option someone else suggested, you could have the person in a cabin on the edge of a cliff or next to a river to explain why no zombies come from other directions.
If you want a plausible story for the character to stay there night after night, you could go with the "waypoint" idea: your character is defending a safe house for slower, exhuasted or injured travelers, and is more skilled with handling weapons than others are.