Waitakere Primary School is without power, phone lines or mobile coverage, and has limited toilet facilities.
At Three Kings School the power has been restored but it remains closed because of safety issues from fallen and cracked trees.
In Waikato, Te Kura Kaupapa Māori o Te Puaha o Waikato is closed and in Wellington Karori Normal School and Te Punanga o Te Reo Kuki Airani early learning centre will not open.
This morning, lines company Vector said about 55,000 Auckland homes and businesses were still without power, down from 79,000 last night, and may not have the lights back on for three days.
Vector was aware of nearly 400 outages throughout Auckland, after its network was extensively damaged in Tuesday night's ferocious storm. Hurricane-force winds reached 140km/h in the city and peaked at 213km/h at Manukau Heads.
At the storm's peak, 182,000 properties were without power.
A dozen schools closed yesterday have reopened today.
Some of those schools will be operating without power, including St Joseph's in Onehunga.
Closed schools
AUCKLAND
Henderson Valley School
Riverhead School
Three Kings School
Waitakere Primary School
Taupaki School
Central Auckland Specialist School
Parakai School
Waioneke School
Blossoms Educare (early learning centre)
Loving Care Kindergarten (early learning centre)
WAIKATO
Te Kura Kaupapa Māori o Te Puaha o Waikato
Wellington
Karori Normal School
Te Punanga o Te Reo Kuki Airani (early learning centre)