I'd like a .357 revolver. Seems reasonable, since it doesn't fire fast and I don't have to hunt for spare magazines. And it makes me way less likely to get into a firefight.

Anyway. Ask yourself: if everything went to crap, and you were in a destroyed city with clothes, shoes, and any supplies you can salvage, what would you want? What would be your ultimate goal? "Find more food," sure, but would you want the rest of your life to be just that? 

I would say three possibilities are companionship, refuge/safety, and a sense of accomplishment. So, maybe there's a huge "shelter" that survivors have made and are building. Every Fallout game has one. Think Megaton or Diamond City. Goal: get there. 

To buff it up, they will only let you in if you bring supplies, currency, food, etc. Make a checklist for players to choose from that they don't get to see until they get there.

For companionship, maybe everyone could have a radio receiver and the GM could send out messages via PM or publicly. Locations of supplies or something. This could get players to meet up. In the other one I played, the GM had the "Children of God," which were just a lot of scumbag mercs who thought they were superior because they survived, and they mostly just killed people and stole supplies. The GM used them to move players around, because they had better numbers and bigger guns. They were a good source for resources, though, so hunting them was also an option.

I went into an abandoned apartment building to find a friend. They weren't there, and I had no good leads. To help, the GM sent a group of the CoG in to ransack the place. It gave me a goal (get the heck out of there). Wild animals and earthquakes could be utilized as well.

Sense of accomplishment comes from players doing something the GM wanted them to do. Could be saving lives, I dunno. My character goal was to find his BFF, but I had nothing to do after that.
-----

That's all I got for now. Your RP will end eventually, so you might as well have an ending. We're writing a story, and I would rather have a planned ending in ten pages than "no one is posting so I guess it's over" ending in 50 pages, even if the ending is something simple like "Everything's going to be alright now."