What is the F(&(*&(ing zombie rubbish?
Why is every game and TV series in the world obsessed with zombies?
I really don't get it. Change the damn zombies to aliens or just humans competing for resources and I might be interested, but I automatically avoid anything with the word "zombie" in it.
If you need inspiration, read.
Twilight 2000 was a game set in a post apocalyptic world and featured a rich game world (without zombies)
Traveller (a pen and paper far future rpg) has whole books full of scenario ideas and even a random encounter generation system.
If that doesn't work, go to a more engineered system. You want the player to be able to use a crossbow, so he needs to be able to make string, he needs tools to work wood for the stock, he needs metal to hold it all together, he needs bolts to fire. Each part of the process can be turned into a small scenario. Hell you can have several different scenarios for each part with varying results.
1) Kill a mutated tiger and use it's guts to produce string (range +3)
2) Battle your way to a sacred grove where a plant grows that can be spun into string (range-1, damage +1)
3) Capture mutated sheep and farm them for wool to use spin into string (range-2, damage-1)
4) Destroy an old building to extract wiring from the walls that can be spun into the string (range+3, damage+3, 5% chance of missfire)
It's up to you. As TheNut says though, you need the engine first.