But the journey takes a sour turn, when they get flagged down by a road police officer.
"Guys, we got pulled over by the police," Cole says into the camera, as the blue and red lights flash in the background.
"I don't know what the rule is in New Zealand, do we get out?"
Cole gets out to speak to the officer.
His girlfriend, Raya, is shown telling the officer she doesn't have a driving licence.
The police officer then tells the pair they were travelling at 141km/h - an offence which usually sees your licence suspended immediately for 28 days.
Cole later gets back into the car after the police officer says he will think about what action to take.
"Oh dear, oh dear," he says as he gets back into the driver's seat.
"I didn't even know we were going fast, I was just cruising, just chilling, just chatting away.
"Guys always watch your speeds," he adds to his viewers.
But then he admits: "I don't even know what the speed limit is in New Zealand.
"I'm not used to kilometres."
The speed he was clocked doing - 141km/h or roughly 87 miles per hour - is also over the UK speed limit of 70m/h (112km/h).
Cole said he informed the officer they were rushing to get to a friend's house in time for dinner.
When the police officer returns to their window, he tells them: "It's going to be an expensive dinner," before explaining that he's written the ticket for 139km/h so he can keep his licence.
But he must pay a fine of $400.
Afterwards Cole tells his fans: "I have learnt my lesson, I'm going to be driving a lot slower, and abiding by the road laws in New Zealand. It's a very expensive lesson to learn."
The fine means they can continue their adventures in New Zealand, he says.
Cole's video comes after a year in which the issue of foreign drivers has hit the headlines here, with fatal and serious crashes and other incidents involving bad driving behaviour.
