Authorities said they were considering sending ferries to ship the holiday-makers out of the remote South Island region after huge landslips closed the main highway.
Elsewhere, the storm cut power to tens of thousands of homes, felled trees and washed away roads.
Cyclone Gita caused extensive damage as it tore through Tonga and Samoa last week, peaking as a top-of-the-scale Category Five super-storm.
It has since been downgraded but still carried a sting in the tail when it reached New Zealand overnight, bringing 140 kmh (90 mph) winds and around 200 mm (7.8 inches) of rainfall.
Seven local council areas, including the South Island's main city of Christchurch, declared a state of emergency on Tuesday as officials anticipated the worst.
Most reported early Wednesday that the weather had not been as extreme as predicted, with the top of the South Island the worst-hit area.
Local mayor Richard Kempthorne said all transport options would be considered if road access to Golden Bay could not be restored swiftly.
"Ferry and barge and for some people air travel... we've got a population of 5,000 people who need to eat and we've got holidaymakers," he said.
"There's probably hundreds if not more than 1,000 people in there at the moment who probably want to leave and continue with their trip."
The official MetService weather bureau said the storm had moved out to sea south of Christchurch by mid-morning Wednesday.
