"Resources" - food, ammo and the cheap treasures. What they are, where they are and how can the PCs get their grubby hands, claws and tentacles on them?
For sandbox play I feel it's important for resources to be scattered about, each town should not have a general store that supplies most adventuring needs. Enforcing travel, risk and contact with NPCs keeps the campaign busy.
Start cheap. I'm all for limiting the amount of starting equipment available. It supports the scavenging/scrounging limited stuff model of post apocalyptic adventure and gives the players early and clear goals. You want to see a motivated player?: have all but the lowest grade of armors be too expensive for initial purchase.
Food. Lot's of folks gloss over this to some degree, food is heavy, takes time to prepare, is sought after by everything else that eats and it goes bad too. A case of cup-o-noodle is a pretty good haul for a post apocalypse scavenger, ready-to-eat and self-heats are even higher value hauls. I like to keep track of food in "meals" and track the use of these meals. Put a random encounter chance on eating/preparing different foods and what rations the players pack becomes more important then scribbling "Iron Rations 1 Week" on a sheet. Another trick I favor but use nowhere near as often as I like is putting food going bad and other food related events on random encounter/event tables; it can sound minor but in campaigns where it matters "bread grows mold" is a fairly notable occurrence and will bother penny pinching players more then 20 mutant tribesmen would.
Freshpond is the place to go for fresh food but that requires one to avoid offending the locals and dealing with an active militia force.
Water. Three days without water and you are probably dead. People need a surprising amount of water to stay healthy and active. Less then a quart a day is almost as bad as no water. Most adventurers are going to need 2 quarts or more a day, even more if they have mounts.
I've got a lot of water sources on my mutantbox map, deciding where to collect it is something the players are going to have to learn. Would you drink water from a pool in the tar-pit? Is it safe to drink out of the centuries old cistern? Can you drink acid rain (you know that really dangerous RPG acid rain)?
Ammo. Sure you got a bow, crossbow, musket or SMG but just where does one get ammunition?
The presence, manufacture and availability of ammo can play a biggie on choice of tactics and influence where and how far the PCs will wander.
Spillside is the place to go in my MutantBox if one is looking for blackpowder, this requires travel, dealing with wily merchants and dangerous gangs of toughs to get a large and economic supply.
Wild Goods. The goods of the wild wastelands and all they offer will certainly keep players busy and on the move searching out supplies. Some mutant powers could carry over to the hides or other goods scavenged from the remains of mutant kills; surely leather armor made from the hide of a gamma sloth has more going for it then then that made from some three horned cows.
The mutant berries I've posted in my blog are a resource to be sought out with some recognized value, some of them require processing and these secrets require PCs to learn them from NPCs.
Recreational Consumables. Drink, smoke and stupider ways to abuse ones own body for entertainment have been popular since the birth of civilization (I once read that bread was invented as a mobile beer kit instead of as a food source itself at first). These make great bargaining devices, moderately portable treasures and some players just can't be kept away once they discover they are available. Who makes them, where they are stashed and how much you can score the goods are again a reason to keep the PCs moving and involved with NPCs.
To keep resources important have NPCs treat them like they are important. The old RPG hooks of monster X is threatenign the village, the caravan needs guards and we need macguffin X from village Y but no one has come from there in a while all require resources someone in the campaign cares about. If that someone who cares is the players then the campaign can acquire a life of it's own.