A few things might make a character choose a ranged melee weapon.
Cost; guns and bullets aren't cheap, except for the Courier. I'd imagine some bows could get very expensive, so maybe that's moot. But you can reuse the ammo.
Stealth; Fallout silencers work like Hollywood silencers (impossibly well), so this may not be a factor. Still, a bow's pretty quiet.
Personal preference; why is my home state overrun by bow hunters in the Autumn?
Machismo.

Guns seem plentiful to us because we are the Vault Dweller/Chosen One/Lone Wanderer (& friends)/Courier. We go places and do things that no one else does. The average post apocalyptic Joe doesn't wander all that much. To be fair to your point, though, I admit that any schlub wandering around the perfectly safe Boulder City area can grab a Hunting Rifle, a Service Rifle, a Combat Knife & Ammo at absolutely no danger to themselves.

I'd just like to point out that you can get levels of silence approaching "Hollywood silence" with the right weapon and the right ammunition. Too many people think you make the weapon silent just by screwing a silencer on it. No. Not many realize that a large portion of the "Bang!" of a gunshot is actually the bullet traveling at supersonic speeds and creating a sonic boom behind it... subsonic ammunition is an absolute must for silent shooting. Most of the world's "Hollywood silent" weapons are also integrally designed to be silent, and their silencer is far larger and better adapted to the weapon and the round being fired than modular screw-on-the-end type silencers. (Also, unless specially designed to work with subsonic ammunition, most self-loading firearms will NOT cycle when firing it because of the lower pressure thus requiring the operator to cycle the action after each shot.)

Just saying. Nearly silent firearms is not fiction, Hollywood just glosses over some important details and make it look easier than it is.

Actually, most of the bang is from powder explosion and rapid change in pressure in from of the barrel; the sonic boom of the bullet is rather small because the bullet is....

Cossbows/Compound Bows would to be melee weapons. They would be a projectile weapon because they are projectile weapons and would go under guns.

http://www.youtube.com/watch?v=McStH6Vz6V8 The loud "Crack!" is the bullet flying at supersonic speeds. The dull "thud" after it is the muzzle blast itself catching up at the speed of sound. Also examine http://www.youtube.com/watch?v=socgmULGVOA which demonstrates the *enormous* difference in sound between supersonic and subsonic ammunition in a suppressed rifle.

Actually tomahawks would fit in Mojave desert moore then Crossbows and bows.