Hmm... maybe GURPS with a low point-buy in. 3e suggests that a gritty, realistic WW2 game, in which players will die, use between 50-75 points (and a GM determined limitation on negatives/flaws). Make combat nastier by using fright checks, bleeding rules, infection, and maybe some body-hit locations. Regular GURPS can be a bit rules-heavy if I remember properly but GURPS Lite only has fright check rules as far as I'm aware, so you may need to some adaptation.
With 3e rules, start out at the current TL7(6), the 7 being what we are effectively at now, and 6 to be a world that has suddenly lost it's computers and electricity. At the start of the game, all that nice TL7 stuff is around to help out: but that's finite and will eventually break too much to be effectively repaired. Players can either keep regressing in TL or try to reinvent/adapt technologies within their local areas to keep up a somewhat modern TL.
As for missions and such? Survival and resource acquisition are the most obvious. If you're in the mood for them actually doing something sort of heroic, they could try to find the source of the plague (presuming that nothing that spread and killed so fast is natural) to bring the perpetrators to justice.
Personally, I'd have them try to create their own community and then let them run with it: they can set one up where they are or travel cross-country to a better spot, do they want to be hunter-gatherers, agriculturalists, raiders, or some combination of these? What happens when the supplies they were gathering run out? Do they just regress in TL or try to keep it maintained within their community? What about if other people hear of their success and want to join? What if raiders hear about their weakness? If there are interpersonal conflicts between the players, then all the better.