what school best studies child development?

I don't like quoting other sites but here is a link to the best colleges for Child Education degree programs. Included are the usual suspects like NYU, Boston University and Vanderbilt.

https://www.niche.com/colleges/search/best-colleges-with-early-childhood-education/

For me finding schools that had good specialized fields of study was difficult since they were just listed as Psyche majors. Doesn't completely answer your question but I think a good place to start would be with schools that are known for having good psychology programs. From there after you form a basic list you can look deeply into the schools and see which allow you to specialized in child development.