This is a bit old, but this 2014 post dealing with the demographic decline of Lower Fairfield County shows the decline in children is not just an issue unique to cities. Very wealthy towns - well known for top-notch school districts, saw declines in the number of small children of up to a third in the 2000s alone:
The author attributes this in part due to the sort of "snob zoning" common in established suburbs in the NYC metro. High housing costs coupled with this snob zoning mean there simply aren't many starter homes to go around. As a result the average age in these towns continues to climb, with many towns well known for "excellent public schools" having median ages of over 45.
There's a reckoning coming in these areas in the 2020s and 2030s, when the boomers who have aged in place die off en masse