My wife and I stayed in nyc when we were young. With kids now, we are thinking of coming back because of the schools. What is the best way to research the schools that you mention above assuming no prior knowledge.
For public schools:
https://schoolzones.us/nyc/ https://www.schooldigger.com/
NYS tests all their schools. A school which is in the top 10% of the NYS testing would be considered elite. Top 20% is good. The majority of NYC schools are bottom 50%.