Which city? In NYC, a stand-alone townhouse in need of TLC with any outdoor space would probably start somewhere around $4-6 million (Manhattan). $2-3 Million in the outer boroughs (the ones that are up-and-coming, some of the gentrified neighborhoods are approaching Manhattan prices). All of those neighborhoods have poor public schools (yes, I know there are exceptions these days. But they are just that - exceptional. Not the norm). You would most likely have to send your child to private school. Minimum $20k/yr/child starting in kindergarten. Many push $40k/yr/child.
In surrounding suburbs with top public schools and ~45min rail commutes, a well-kept ~2k sqft house would be around $700-800k. New construction with all the trimmings: $1m+.
For many, this isn't really a "choice".