What makes a good school?

What makes a good public school? Standardized test scores are often used as a measure. California uses these to create "API scores" However, this can favor schools that "teach to the test", as opposed to ones that actually teach. It also does a poor job measuring smart kids. (They would probably ace the test with no teaching.)

AP test scores are the measure preferred by US News. These do a good job of measuring the advanced work that the schools do in preparing students. However, there are still plenty of ways these could be misleading. A school with many smart kids may have lots of AP test takers, even if instruction is subpar. It can also show institutional bias. A school that offers a lot of AP classes will perform better school that doesn't push AP tests. It also only does a good job with the top students. And, it is only applicable to the upper grades of high school.
In the same vein as AP test, college admissions could be used. This is, after all, a common end goal for high school. A school that sends lots of students to your college of choice may be ideal. But, it tells little about the quality of instruction.

Unfortunately all of these measure achievement, but provide little clue of the actual quality of instruction. An ideal metric would take the "inputs" in to account also. How could that be done? The income of the families in the district could be used as a guage. Unfortunately, this can be difficult to accomplish. Using district-wide median income may skew results (especially for large districts). Using school-area income may be reasonable for neighborhood schools with no out-of-area transfers. However, isolating the appropriate area, and finding the data could be challenging. And finding schools that don't have any out of area transfers could eliminate a great number of schools.
There is also the question of what data to collect. Income seems like a straightforward one. However, the comparison range must be taken in to account. A high-income area in South Dakota might have a lower income than a lower-income area in Silicon Valley. The reduced and free lunch statistics may be useful. But, they only account for extremes. Education levels of parents, race, English ability, and parents status are all factors that can be taken in to account. A good measure can try to create an equal base and compare how performance compares to expected performance. This may identify some exceptionally performing schools. However, especially at the "high parent involvement" end, this wont tell much. (Parents and tutors may compensate for poor education.)

Is there a good way to quantify school quality? Do we have a lot of really bad schools that appear to be good simply because parents care?