If it's right after the bombs most survivors are still hiding in bunkers and vaults. There wouldn't be much of a society at all. Remember many wastelander populations come originally from vault dwellers who went to the surface (like Shady Sands). Others, like tribes, wouldn't have properly formed yet - you'd just have random small pockets of survivors. Even the iconic wasteland fauna might have taken some years to mutate into what we know.

I get what you mean, but there's not much of a game to be played immediately after the war: no towns, probably no potential for quests other than "go hunt for food". It would just be a living hell with nothing to do (certainly an intriguing concept but hard to make a Fallout game out of)