Also you nailed it on the property tax point. Often overlooked as the biggest issue with education. A similar sized home in a good school district can be 2 or 3x as expensive as one in a mediocre school district.
Edit: when talking about property tax, I am referring to most suburbs, not NYC.
Seems like a lot of people are posting evidence that the property tax point is correlated with better schools but the funding difference is made up for by the stare and federal government. Interesting.