What with this? Not a post apoc theme, but fighting with bow and arrow could be very popular in the Wastelands. Why must everyone have a HK416 in the new old-school game?
Whilst I'm pretty sure that whoever desgined Daryl's character on The Walking Dead basically said 'let's take Sawyer from Lost and put him in a zombie apocalypse' and then stopped work for the day, it sure does a good job of making the crossbow look like a viable, and situationally superior, alternative to a gun - stealth kills galore and can always make more ammunition.
[I'm also pretty sure that the writers have written him into a hole for next season. Too similar to Miccone to have both characters present simultaneously, but haven't given him enough of an arc to make killing him off interesting (c/f the end of Boardwalk Empire season 2 - it works not because the guy is the 2nd main lead, but because by the time he goes into his final "I thought you knew. I died years ago, in the trenches...." monologue you've already spent 2 seasons slowly realising that the guy is a walking corpse who just wants to put a few things right before biting a bullet. As much as I enjoy The Walking Dead, by comparison, the writers are incapable of developing more than one character at a time - this season we had Shane ala the first run of the comics, with a tiny bit of characterising Glenn (even Rick is a pretty poorly developed character) - you need more than that for a show to stay interesting past the first 2 seasons).]
Back on topic, surely bows (going from simple to mechanical Olympic bows) and crossbows would be the 'modern/post-apoc' version of the fantasy thief's dagger? I mean, all characters could have uses for melee weapons (even in current military scenarios, unless there's artillery, MG or air support to keep people pinned, a lot of killing is at melee/bayonet range, and they still train the fuck out of it for that reason), but in a post-apoc setting, a 'stealth guy' isn't going to be a professional thief - he's going to be a hunter or a woodsman, who wants to track, silently pick his way past a gate without alerting his prey, and pick off a deer or two for dinner without creating a ruckus (that will drive the herd away, or worse - attract human scavengers). Bows and crossbows fit right into that.
Also, with the 'not a post-apoc' theme. Taken seriously, there's no reason why it couldn't be PART of a post-apoc setting. Look at Chernobyl. Ok, you want the urban wasteland to dominate the setting for thematic reasons, but there's going to be low-rad areas where a few decades later wildlife is thriving now that the human menace has retreated. There SHOULD be forests and wildlife in pockets outside the urban areas - after all, the nukes will be aimed at the cities and military outposts, so any travelling outside of those areas should lead to renewed forests. It's one thing that STALKER got right, simply by copying the Chernobyl area outright. I wouldn't want a whole game set in a forestry area if it's post-apoc, but it could certainly be part of the game-world.