Hey Gilles,
From your screenshot and what you've described, I see a very simplistic city builder as the foundation for the game. At first, your people just go out and gather/scavenge for food and water, but then those things become integrated into the city as farms and wells. Traffic would be the people walking to and from, delivering the resources around... as well as patrolling guards, builders, etc. You'd need homes, farms, walls, barracks, etc. Paths (roads) take time to make, but allow for faster travel, otherwise people walk slowly through the landscape as they see fit. Players get to control how many people are recruited for certain jobs, but you never directly control them. You choose what and where to build things, but how effective they become depends on the availability of resources and the traffic congestion levels. I think if players controlled the people, it might be too similar to classic Warcraft, but keeping the game-play similar to SimCity with a simple resource gathering component, might be more interesting.
And then, of course, there would be dealing with attacks on your city. These moments would create the chaos needed to make city design and upgrade choices a constant mix of do I build/layout for defense or expansion. Build too much and your hard work is destroyed, but defend too much and the strength of the attacks become overwhelming. These attacks would take the form of tribal warfare, resource stealing, sabotaging your paths and buildings, poisoning grain and water, mother nature, etc. The frequency of conflict is key.
As far as a post-apocalyptic setting goes, would people be inhabiting old ruined cities? How much technology survived? Is it back to the stone age, but with mohawks and sunglasses? Would vehicles play into it, like Mad Max? Do the people need entertainment, like brothels and gladiator arenas? Are you the "mayor" of this city?
Anyway, this is all just food for thought. Personally, I like the idea of a simulation over a typical RTS. Watching a city evolve in somewhat unpredictable ways on it's own has a lot of appeal to me, especially if the remnants of certain things lingered long afterwards. Dead bodies littering the fields, burnt farm lands and forests, land turn up a bit from an earthquake. Seeing the story of your survival in the landscape itself, basically. And that's all I got.
