In Ontario, Canada, the public spent $23.6B on education in the 2013-2014 fiscal year. That's total cost, including salaries and building maintenance and supplies and everything else that goes into running an education system. That works out to $11.7k per student per year based on 2,015,411 students in the 2013-2014 school year.
That's similar to what you'd pay in private school tuition, and that's with all the bureaucracy and unions and teacher's salaries (teachers here top out at around $100k salary) and all the other things people complain about as reasons public schooling is a waste of money. It's not; it's about the same cost as private schooling.
But with public funding, a good education is available to everyone, and the public has more direct oversight of the curricula and of standards. As a result, Canada scores well in international school rankings, similar to the best European countries -- which are also, almost universally, funded publically (https://en.wikipedia.org/wiki/PISA_2012#Results).
Canada, Finland, Singapore and South Korea are some of the exceptions as far as I remember.
True for public schools.
2) Funding often comes directly from the local school district, most of which are already severely cash-strapped. The problem here is that the cost of a single student attending a school district is largely buried in fixed costs: when the state takes $6000/yr from a district and gives it to a charter school, the district's costs do not decrease by $6000. This makes school districts worse, which accelerates flight to charter / private schools.
Open enrollment causes the same issues.
3) Educational standards are different -- Also, most states offer some sort of funding incentive based on test scores -- which just encourages schools to play the numbers game by finding reasons to suspend/expel struggling students, encourage cheating on tests, etc.
True for public schools.
Public shools in NY are zoned so if you want your kid to go to that good school in Tribecca you most probably have to move there.