Find schools by neighborhood or CD on NYC Facilities Explorer main page, scroll down to "Build a Custom Search" and filter by type of facility, click "education, welfare, and youth," then "schools K-12." Then scroll further and click "view selected features"
Then where it says "filter by administrative boundary," choose neighborhood or CD, and then the specific CD or neighborhood itself, facilities appear on the map. On the top right you can download the filtered data into a CSV file. Most of the schools list a capacity.
PropertyShark - Sign up for an appointment to use PropertyShark. PropertyShark has a trove of info on buildings, landlords, reveals the real owner of a building, some tenant contacts, links out to DOB permits and violations, and mortgage and deed documents from ACRIS. Also has recent forclosure actions.
Search the links above for NYC Community District Profiles NYC Population Factfinder - (Neighborhood data)
Scroll down on main page at NYC Facilities Explorer to "Build a Custom Map." Then filter by type of facility, and scroll further down to click "view selected features."
Then Choose Type of Area (neighborhood, CD) and then the Area itself, facilities appear on the map.