Matthew Yglesias points out
a paradox: If schools in one region start to improve, then all the rich families will move in, property prices will shoot up, and all the poor families will have to leave. Thanks a lot, eduwonks. On a related note, I'd add that the "bidding war" for houses in neighborhoods with good schools gets brutal on the middle-class pocketbook. But bid parents must, since the main consideration for any family buying a house will be the local school system.
But the solution here is fairly obvious: Sever the link between where a family lives and where a family sends its kids to school. Institute some sort of public school voucher system that allows families to send their kids anywhere they want within a district or reasonable geographic location. Families can then live in crappy neighborhoods and still
send their kids to good schools elsewhere. And, conversely, if a school in some crappy neighborhood suddenly becomes excellent, the only thing that will happen is that some high-achieving suburban kids will get sent to the school—which would only improve the school without the gentrification effects Matt's talking about.
Ideally, by the way, public school choice would operate within certain boundary conditions—for instance, each school has to set aside no fewer than 10 percent and no more than 30 percent of seats for kids who qualify for subsidized-lunch programs. Or whatever works. Unfortunately, there are also real commuting issues here, and how to ensure that, say, property tax revenues get to where they need to go. But this is why we have think tanks, hoho...