In about 49 states (Hawaii being a notable exception), public schools are run by local districts. The districts may be units of city/town government, or of a county, or be independent districts. But they're always smaller than the state. This is an old American tradition that people treat as a good thing, but which is really incredibly expensive and harmful in many ways. It's not just education that suffers, either.
Local school districts cause all sorts of issues. Inequality of education is only the most obvious. Some states have had major lawsuits over it. Since schools are largely supported by local taxes, wealthy districts have more money for education and thus can have a lower tax rate while still spending more.
But the impact goes beyond the schools. Since schools are an important attraction for families, those who can afford to live in the wealthier towns tend to go there, while the poor are left behind. This is a positive (meaning self-reinforcing, though the impact is harmful) feedback loop It has proven to be a death spiral for some older cities. Witness New Jersey's 566 municipalities, most of which have their own schools -- often the smaller, urbanized community becomes the poor stepchild of the larger suburban one that surrounds it. Live in the older town and you pay more taxes for less; live in the surrounding towns and pay lower taxes.
Industry moves too. There are cities (like City of Industry, CA and Teterborough, NJ) that have almost no residents, and thus almost no school expenses, and which exist as tax shelters for their industrial landowners. The few residents go to nearby district schools on a "sending" relationship. This doesn't happen in Hawaii where there are no local school districts.
The net impact of this is sprawl. Suburban and exurban towns seek out industry to help pay the property taxes. They have the land; modern industrial developments tend to use a lot of land, with low-rise buildings and big parking lots. There's not a lot of public transit to these outlying areas; the density is too low to support it. The people who work there often move to nearby suburbs, further paving over the remaining open space. And those developments are more car-dependent than the cities that were left behind.
Suburban education suffers too, though not as obviously. A successful large district offers more variety. This does show up in some suburban county-sized districts, like Montgomery, MD, but in the small-district states, the local schools aim for uniformity. By variety I am talking about special programs like magnet schools for arts, science, and advanced academics. Suburban districts too often aim for good test scores, which reinforce real estate values, but not actual education. They're not the same! New York City's district is bigger than most states, and has some pretty bad schools, but it also has a big variety of specialized programs.
Boston's public schools too have largely been left to lower-income families, but they still offer a big variety of specialized high schools including the rigorous Boston Latin. At the same time, the Metco program buses some non-white Boston kids to other districts. That adds some diversity to those districts. But only about 10% of Boston schoolkids are "white", and the program has the perverse and discriminatory effect of allowing the majority of Boston families (African-American, Hispanic and Asian) to apply to other districts, while the "white" minority either attends local schools (many of which are substandard) or pays for private school. The result is "white flight" among the working class, while wealthy white families and especially childless people who don't care about public schools pay a fortune to live in the tonier parts of town. In fact, there are no public schools at all near Beacon Hill!
The easy fix is to just make the state one big school district. Have local advisory boards, but fund centrally. Allow parents to apply to whatever school they want their kids to go to, noting that transportation routes create natural limits on choice (unless the parents arrange all travel). This would end the tax disparities. Suburban real estate values might fall a bit and urban values rise, but overall costs would go down and the state overall (at least residential taxpayers and parents) would be better off. By not encouraging people to move to the suburbs to get into the school of their choice, we'd reduce energy consumption and have more land left for local agriculture. Better education? Sure, but that's just the start.