Inside, the open interior is a mixture of irregular angles, the lobby walls lined with slanted wooden panels. There are two galleries upstairs, with one hosting a changing schedule of exhibitions — right now it’s the fascinating Ocean Liners: Speed And Style (until Feb 24, £6 to £13). The other, permanent, gallery showcases the story of Scottish design — and I fall for the softly lit charms of Charles Rennie Mackintosh’s ‘lost’ 1907 Oak Tea Room, which hasn’t been seen for 50 years.

The new museum is the first Design Museum in Scotland and the first UK V&A outside London — and it makes sense that it’s happening right here. Dundee, birthplace of DC Thomson comics like The Beano as well as era-defining video games like Grand Theft Auto, has a rich history in design. (As I stroll through the town, which is peppered with public artworks and street murals, I’m chuffed to spot statues of Dandy character Desperate Dan and creatures from 1991 game Lemmings.)

Yet for all its gorgeous gothic architecture and impressive natural setting, Dundee — a Unesco City of Design — can also be rough around the edges. Formerly a shipbuilding hub and the centre of the jute trade, following the decline of these industries it faced some hard decades.

Nevertheless, places such as the Guggenheim in Bilbao have shown how a single cultural centre can create ongoing ripples of confidence and innovation in a regenerating city. The belief is that the new V&A will do the same for Dundee — and it already feels like an exciting place to be.

It’s also rammed with abandoned industrial buildings ripe for renovation. I stay at Hotel Indigo (doubles from £89, hotelindigo.com) in a former linen mill, a chic and cosy place which riffs on its industrial past with pendant lighting and exposed piping. I take a tour around 71 Brewing (£12 including a pint, 71brewing.com), Dundee’s first brewery for half a century, housed in an old foundry. Afterwards, sipping a delicious craft lager, I watch street artist Rogue One spray a mural in the yard outside.

The lanes of downtown Dundee too are filling with cool and quirky independent shops — Exchange Street alone is a good place to cover all my bases. I grab a brew from Daily Grind (coffees from £1.80, hardgrind.co.uk), a friendly coffee shop attached to a barbers, eat a jerk jackfruit wrap from Simpson’s (£7, facebook.com/simpsonsdundee) and have a browse at Oh Hello Vintage (ohhellovintage.com), with its dreamily kitsch pink and green interior.

With two universities, Dundee has a massive proportion of students, and the long Perth Road, stretching west from the centre of the city, is a good shout for indie shops and fun boozers.

I take myself, however, for a tipple at retro-styled speakeasy bar Draffen’s (cocktails from £8, facebook.com/draffens) in the basement of a closed department store (you’ll be greeted by mannequins on your way in.) The bar doesn’t have an official website or like to give out its address but it’s easy enough to find (behind an inauspicious-looking door down a slightly daunting back alley) if you ask a local how to get there. If all else fails, just follow the sound of jazz.

People in Dundee are no-nonsense, funny and friendly — and rightly proud of their city. I came for the V&A but now I’m not sure I want to leave.