New York will make a final decision about reopening schools this fall at the beginning of August. Governor Cuomo says the state's 700 school districts need to submit their reopening plans by July 31st, and the state will make decisions whether they can move forward by the first week of August.
Cuomo also announced Wednesday that indoor malls can re-open on Friday everywhere in the state other than New York City, provided they have certain air filters in place. The governor explains air filters rated MERV-13 can filter out tiny particles, including the COVID-19 virus. This order will apply to all malls located within regions undergoing "Phase Four" of the re-opening process, which as of today includes every one of the state's regions, other than the five boroughs of New York City.
There are other ventilation protocols required as well, while it's not clear if this will be extended to places like gyms or movie theatres, as some are specifically concerned about air conditioning systems within those locations.