Edit: let’s keep kindergartners and pharmacies separate and discuss how to improve data about pharmacies here:
If this kind of format works then there is Ravimiameti tegevuslubade register that lists every pharmacy:
https://rkav.tehik.ee/rkav/faces/pages/tegevuslubaForm/tegevuslubaOtsing.xhtml
Currently it looks like almost 100 pharmacies are missing from OSM.
I assume there are no licensing issues with this kind of public data:
https://www.riigiteataja.ee/akt/121122017016?leiaKehtiv