Are small towns "rural" or "suburban"?
Rural, I would think -- though personally I'd argue that they should be a category of their own.
The Census Bureau identifies two types of
urban areas:
Urbanized Areas (UAs) of 50,000 or more people
Urban Clusters (UCs) of at least 2,500 and less than 50,000 people.
“Rural” encompasses all population, housing, and territory not included within an urban area.
So urban clusters (=small towns) are not rural, since they are a form of urban areas.
In Europe small towns are urban, I would think that was also the case in the US. It makes little sense to call them suburban.