These always looked like fun, I'd love to try one some day. I'm in Auckland though, so no help for you in Wellington, hopefully you find someone!

For people interested in Escape Rooms there is the ANZ Escape Room Enthusiasts Group @ https://www.facebook.com/groups/600731090104609/

And there is the New Zealand escape room Meetup Group @ https://www.meetup.com/New-Zealand-Escape-Room-Group/

There are 30 Companies in New Zealand and 100 in Australia with over 300 separate themed rooms throughout the 2 countries