I noticed that houses in Tarrytown with Irvington school are priced higher than houses in Sleepy Hollow. I also think families are much more apt to buy houses in places with good school districts rather than those that are not. I have been looking to buy in Westchester and I noticed that open houses in Chappaqua, Scarsdale, Edgemont are bustling while open houses in other areas are quiet.
That said, the school district's reputation is often linked to SAT scores which may or may not be a good indicator of the school curriculum or teaching methods.
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If there's only a slight or moderate gap, and that's the perception, then there won't be much difference. Also, obviously it matters to parents of children in public schools. If the demographics are such that most of the buyers don't have school-age children, it won't matter much. Or if it's fairly common for buyers to send their kids to private schools, then they won't care much about public schools, either.
And keep in mind that there's often an inverse ratio between property taxes and school quality. Not always, but often. That is, the higher the property tax, the more money goes to the schools, and thus the higher perceived quality of the schools. So you might have a situation in which a seller is balancing high property taxes and high perceived quality of schools against more affordable property taxes and medium perceived quality of schools.