I am trying to trace a man called George Douglas Cochran who lived in
Queenstown in New Zealand in the 1950s and 60s and who was the Mayor
Of
Queenstown.  He had a company called Cochran Enterprises Unlimited. He
moved to the North Island of New Zealand sometime after 1962.
Can you give me some help as to how I might trace him or his children
please?

You could ask someone in New Zealand to look for his name on the
Electoral Roll. It can't be done online.

Otherwise, there's just the White Pages:
http://www.whitepages.co.nz