Not just to Arrowtown, but to a particular shop that sold a particular product: a lamb and mint pie.
Unfortunately, the Arrowtown Bakery and Cafe had not been scoped out beforehand, nor had the proprietors been warned that the Australian prime minister and her partner, and New Zealand Prime Minister John Key and his wife Bronagh - not to mention 20 hangers-on, staff, police and media - would visit their establishment on Saturday afternoon, in search of a lamb and mint pie.
It was still on the menu and still so popular that it had sold out on Saturday. Mr Mathieson had to be content with a hot venison pie and a squeeze of tomato sauce.
Ms Gillard was feted in the preserved historical gold-mining town by locals, children, travelling Australians and Australian immigrants to New Zealand.
Pete Gawron, the founding owner and chef at Saffron restaurant, was originally from Adelaide and had been in New Zealand for 14 years.
''I miss the beaches in Australia but this is an extraordinary place, and we get four seasons here,'' he said.
''In Melbourne we do that in a day,'' Ms Gillard replied.
There was one noisy upset from a small boy named Kalem, who was intent on wresting from Ms Gillard a kiwi toy which a shopkeeper had just presented her.
In an instant, Ms Gillard knew that giving away a kiwi would create even more upset to her hosts - so she gently but firmly held on to the toy.
It was a picture-book walkabout in a picture-perfect town. Even the local Harley-Davidson chapter were welcoming, and offered Mr Key a go on one of their machines.
An earlier visit to the Queenstown War Memorial was not quite as perfect.
During a wreath-laying ceremony, Mr Key appeared to have difficulty keeping his eyes open for a couple of minutes.
He kept rubbing his eyes, but no sooner had he opened them than they would shut. He said later, through a spokeswoman, that the problem was because of the glare on the war memorial, which made his eyes water.
It was about 24degC and bright sunshine but he did not look in danger of fainting, as he did several weeks ago at a Christchurch restaurant.
The ceremony was watched by a couple of hundred people, and both prime ministers were warmly welcomed and applauded when they drove away.
A protester, who would give her name only as Fay, held a placard saying ''Close Nauru''. That was a reference to the island nation that hosts one of Australia's offshore processing centres for asylum-seekers, which Ms Gillard has reopened recently. The prospect of being detained on Nauru for years is designed to deter the arrival of boat people.
Mr Key on Saturday agreed to take 150 refugees a year from the offshore processing, within New Zealand's annual quota of 750 refugees.
He said it recognised the intelligence and support on illegal arrivals New Zealand received from Australia.
By Audrey Young, of the New Zealand Herald.
