Rural isn't a definition so much as it's an idea
A quick joke: A farmer wants the most efficient sheep pen possible. It must hold the most sheep for the least amount of fencing. The engineer says it's a rectangle because sheep are rectanglularish and so the most sheep can be put into the pen. The physicist says it's a circle because that maximizes area with the least circumference, minimizing fence cost. The mathematician, on the other hand, steps up, quietly draws a circle around his feet and proudly proclaims, "I declare everything outside this circle to be the pen." Why is the joke important? because this is the kind of answer you're about to get.
The U.S. Census Bureau has a remarkably practical definition of "Rural."
For the average American, rural is an abstract concept of rolling hills and farmland rather than a concrete definition. Thus, it can be a difficult task trying to define the term "rural" and an even harder task trying to explain it.
The Census Bureau defines rural as any population, housing, or territory NOT in an urban area.
OK, so what's "Urban?"
Today, "urban areas" consist of two types of geographies:
• "Urbanized Areas" have a population of 50,000 or more.
• "Urban Clusters" have a population of at least 2,500 and less than 50,000.
The problem with defining words like "urban" and "rural" by population density is that population density is variable. Really variable. In one square kilometer you might have 20 people. In a second, you might have 2,000 people. A square kilometer is a really big chunk of realestate, so both can be considered rural.
What the U.S. Census (and, by extension, the U.S. government, as many if not all departments use the Census' definition) did was define the smallest geometry. In other words, what's everything that's NOT rural, because "rural" is going to define the vast, vast, vast majority of land everywhere other than on Trantor.
This is important for you, too, because the vast, vast, vast majority of your land is rural (or wilderness). So, the real question is, "What's urban?"
If you define (in your world) "urban" as any small location filled with people and buildings containing merchants and more than a couple of families, then you've won — because everything else is rural.