The story by Michael P. Kube-McDowell is interesting although not great. The first part follows two scientists preparing for what appears to be a looming nuclear Holocaust. The second part focuses on the female leader of a very small band living primitively, without purpose. There have been many depictions of both scenarios, but both the specific concerns of the scientists for survivors and the issue of human creativity and purpose as handled here are interesting.
The Election by Robert Silverberg is a much-anthologized classic, giving a possible situation in a devastated U.S.