Not in the US. Public schools are funded and managed by the local governments (usually county or city). So, only residents of those locales get to attend.
You could send a child to a private school in the suburbs, but that's doesn't gain you anything over sending the kid to a private school closer to home. Plus, it costs an additional $6000+/year. That's tuition at my local Catholic high school; it's an average school, no better than the publics in the same area.
<outsider's shrug> From a policy perspective it seems to be a no-brainer then to move school financing to the state level, at least for a part of the schools.
You could send a child to a private school in the suburbs, but that's doesn't gain you anything over sending the kid to a private school closer to home. Plus, it costs an additional $6000+/year. That's tuition at my local Catholic high school; it's an average school, no better than the publics in the same area.