Women have more children in lower cost of living areas where room is more cheaply available. Women have fewer children when there are more job opportunities available to them.
This makes perfect sense. In an area where there's not much cost to having an additional child but there's not much job opportunity for women, the opportunity cost of having more children is not as high.
In the more densely populated cities, rental space is at a premium and the cost of living is much higher, but there are also more job opportunities for women outside the home and more opportunity for women to earn more money. If she has more children, not only is she going to have to worry about being renting a larger home for the family to have enough space in, but the increased responsibilities at home could make her have to forego a high-paying career.
In more rural areas, there is plenty of space outside for children to roam around. Because there is more open land, there is more opportunity for people to engage in minor economically productive activities with this natural capital that surrounds them (growing food, harvesting wood, hunting, as a couple of examples). These are the type of side activities that a larger family size could help contribute to. In the rural areas, there is typically fewer specialized job opportunities outside of the home, so people in these areas tend to do more things themselves. This creates a sort of flexibility that allows children to help economically contribute to the household in some ways.
So even though a woman in one area, or from one social class, may have more money than women from another, the opportunity cost—what she is sacrificing by having children—is higher.
There is one more thing that I have neglected to mention upon. And that is the ability of men to act as husbands to provide for their family. In places where the male un- or underemployment rate is high, like in Eastern Europe or urbanized Japan, female fertility rates will be lower than what they otherwise would have been. When there is a shortage of "good husband material", women are reluctant to get married, reluctant to start families. However, this depends on the culture because there are some subcultures where women may have no qualms about having children without a father. This is common in some parts of Latin America where the peasant workers are highly migratory, or in some poor African-American communities living in urban areas.