There is access to computers, if you don't have your own device at most of the hostels we stay at.
So as long as you have, an email address, or some sort of social media account they will be able to contact you when you have Wifi or are sat in front of a computer.
Make sure to contact them every know and then, they do worry about there cherubs! Parents do contact us, if they haven't heard from you in a while - it happens more than you think - so keep them from worrying and let me know you are safe!
Check out more information before on Wifi and Internet when travelling in New Zealand below: