According to the Governor's Executive Order 205.2, instructions are provided for students and staff returning to school after travel to a state that is not contiguous to New York (that is, states beyond those that directly border New York State):
FROM EXECUTIVE ORDER 205.2
"All travelers entering New York from a state which is not a contiguous state shall quarantine for a period of 14 days consistent with Department of Health regulations for quarantine unless:
For travelers who travel outside of New York for less than 24 hours, the traveler need not test prior to departure from the state, and does not need to quarantine upon arrival.
However, such travelers must continue to fill out the traveler form upon entry; and further shall take a diagnostic test on the fourth day after arrival in New York.
For any traveler who has traveled outside of New York for more than 24 hours, such traveler must seek testing prior to departure from that state, within 72 hours of departure, prior to arrival in New York.
The traveler must, upon arrival in New York, quarantine according to Department of Health guidelines for a minimum of three days, measured from time of arrival and on day 4 may seek a diagnostic test to exit quarantine. The traveler may exit quarantine upon receipt of the second negative test result."
In general, this means that before students and staff can return to school, they will need two COVID-19 test results: one from the state they visited 72 hours before driving home, and another test on day 4 after arriving home. If students and staff don't have both of these, they will need to stay home 14 days counting from when they returned home. An option: they can forego the testing and just quarantine for the full 14 days.