Dunedin is the old Gaelic name for Edinburgh - it is still used in modern Gaelic - and the settlement in Otago was a conscious attempt to re-create Edinburgh in a new land. The main street of Dunedin is called Princes Street. Other streets in the central city are called George, Stuart, Moray, Hanover and St. Andrew. There are suburbs called Mornington and Corstorphine. Luckily the discovery of gold in Otago later generated the wealth to enable the New Edinburgh to be built in a fitting style.
It seems that when raising sheep in the rolling hills of Otago became a big thing, Highlanders were then thought the best people to do it, hence the man with the kilt and the crook. Though, to be honest, most of the Scottish diaspora seems to have adopted tartan-ism as the most obvious signifier of the old country, without bothering to distinguish Highland and Lowland traditions. The motto means 'by following in the steps of our forefathers'. My O' level Latin can't really see that in it but I will have to take the word of Dunedin city council.
The glorious thing about Invercargill is that all of the streets in the city centre are named after Scottish rivers. The main shopping area is on Dee, Tay and Esk streets. Keep going and you come to Spey, Clyde, Don, Forth, Ness. Most poignantly to a Borderer, there are streets named Jed, Gala, Eye, Yarrow, and yes, Tweed. They've even allowed the Tyne to sneak in. The southern gales blow me through a permanent memory of home, a lyrical grid plan of settlers' nostalgia. I can't decide if I feel homesick or I feel at home. Probably the early settlers experienced the same ambivalence.