If I were living in a period of imminent nuclear war, I would consider moving outside of dense urban centers. Was this sentiment common at the time?
"Urban dispersal" was explicitly recommended by nuclear policy planners as a way to encourage continuity of society after a nuclear war, yes. (It is also why the Atomic Energy Commission headquarters was moved out of Washington, DC, to Germantown, Maryland.) There were lots of studies on this. The historically tricky question is whether this actually influenced the observed behavior or not, as opposed to other causes of suburbanization (e.g. decline of urban core, desegregation, etc.).
One article I know on this subject is Peter Galison, "War Against the Center".