We have lived for more than a decade with four children in a house with fewer finished square feet of floor space. I'm curious about what "good neighborhood" means here, because my children can walk or bicycle all over the place, without fear of mishap, and the local public schools here draw people from all over the country. "Reasonable commute" is also a term I'd like to understand better in this context. How tied to location is the employment you each have, if you are able to move out of state?
I have to think that it's possible for middle-class people like my family (at a lower income level, currently, than what you self-report) to live in cities, because we do. Most of our work happens to be in outer-ring suburbs, so "reasonable commute" puts us there, but other people with work nearer into the center of the metropolitan area can live affordably further in.
Disclosure: we live in an other ring suburb of Minneapolis, just outside the beltway freeway around the Twin Cities, and barely within reach of the bus system. My wife and my third son bike-commute often, year-round.