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As mentioned in comments, fallout shelters were of a dispersed nature, being typically located both within existing structures which 'meet the requirements', and in locations built for other purposes, designed to meet the shelter designation requirements.
This document, on the Status of the Civil Defense Program in 1969 discusses locations of 'existing structure' use:
Concerning new construction, again the primary goal was integrating fallout shelter capabilities into applicable regular construction projects. To this end,
So the dual-purpose nature of fallout design was to be accounted for in new construction, just not specifically built structures only built as fallout structures. The last page has some statistics on how many total locations were included:
Farther down the page it discusses the system had representation in 994 counties with a population (in 1969) of over 66 million. The above table mentions over 95,000 stocked locations (those with supplies) and over 108,000 marked locations.