Few other cities roll out their welcome mats quite as extravagantly as Dundee. The mighty River Tay picks you up a mile or so from the city centre and gently guides you in as the rail bridge, one of the greatest feats of British engineering and design, stands to salute you.

From a distance, its cityscape is easy on the eye as it rises from the riverfront, spreads out and comes to rest on a hill. Nature looked kindly on this place and, as if in gratitude, its citizens have since made a speciality of design, of bringing beauty to purpose.

Yet visits to Dundee always seemed weighed down by other people’s prejudices. The buildings in this place always had a civic grandeur and those of us who lingered awhile after football matches at Dens Park and Tannadice were rewarded with fine taverns and a music scene that seemed to elude the radar of the metropolitan arbiters of cool.

Like many of Britain’s great cities of industry beyond London, it suffered depression and neglect as Margaret Thatcher deemed them expendable in her quest to make Britain a satellite state of the global stock market. Bigger and more boisterous cities seemed able to absorb these challenges and even to imbue them with a grim charisma, but Dundee came to be typified by them. Edinburgh could camouflage its edgier neighbourhoods with the shallow glamour of its festivals, while Glasgow’s black humour and gifts of self-publicity rescued it from being disfigured by notoriety.

The announcement that Dundee was embarking on one of Scotland’s most important cultural projects ever, the spectacular V&A Dundee, delighted those of us who have long regarded this great city and its people with affection.

‘Kengo Kuma’s sloping, twisting masterpiece.’ Photograph: Marc Aktins/Art Fund 2019

A year on from its official opening, the vision of those who planned this eight-year undertaking has been rewarded with a steady flow of visitors that exceeded its expectations. The V&A Dundee has been a success and the building itself has become one of Scotland’s most emblematic and instantly recognisable jewels.

When you alight upon it, you immediately become aware of how it strengthens the city’s bonds with the waterfront on which it sits. Thus, the vision of its creator, the Japanese architect Kengo Kuma, has been fulfilled. He said: “I saw a photograph of Scotland’s sea cliffs – it’s as if the earth and water had a long conversation and finally created this stunning shape. Seeing this picture, I thought, ‘Ah, this is the solution’.”

It has also generated a magnificent recasting of the area around it that you must experience personally to appreciate its scale. Here, the limited size of Dundee is an advantage. A five-minute walk from the centre of the city takes you to the gardens that sit in front of the museum. The adjoining hotels and retail developments accord this a destination status that is vital for an economy long bereft of any economic stimulus.

Last week, for the first time, I finally got to see for myself the Scottish design galleries that lie within Kuma’s sloping, twisting masterpiece. Beyond once choosing fonts and shaping text around pictures to make the pages of a newspaper, I have scant knowledge of the alchemy of design. If something is crafted sufficiently well to permit me to use it without endangering those around me then it’s already a work of some genius.

A display room inside the museum. Photograph: PR

Perhaps, then, I was always going to be easily pleased, but for what it’s worth I was enchanted by these collections. Here’s Charles Rennie Mackintosh’s celebrated Oak Room for Mrs Cranston’s Glasgow tea rooms. The fixtures and fittings were rescued before the building’s renovation in the 1970s and kept in storage. Now the glorious, original whole has been reconstructed to provide a majestic close-up of Mackintosh’s sacred genius with light and structure, here gift-wrapped in oak. This alone makes any visit worthwhile.

Of course, there’s much more. Here’s Christopher Kane’s startlingly sensual dresses and the original Dennis the Menace artwork for DC Thomson’s comics. Over there is a three-minute film of modern and sustainable designs for living on the island of Skye and the stained-glass grandeur of Douglas Strachan, one of Europe’s finest masters of the art.

Yet while the response from the public, the majority shareholders in this building and its contents, has been overwhelmingly positive, it has been met with a curled lip from the critics of Metropolis. The cafe is too big, they declared; you can see the metal staples holding the stone slabs together if you look very, very closely; there are not enough exhibits; the views aren’t great. There are plenty of viewing points and, the building itself being the principal exhibit, a wee alfresco promenade around it permits you to see the Tay in all its glory.

One of the guiding purposes of V&A Dundee was to connect the city to its waterfront and to make it not just a grand home for great art and design, but a place where the citizens of Dundee could come to relax and be at peace.

Several visits are required to appreciate this collection more fully and the museum in which they are held. Beyond it there will always be Dundee itself, ever vibrant, warm and striving still to overcome the social problems that afflict other great cities. Dundonians deserved their museum and over time this building and its treasures will evolve uniquely to honour them.

• Kevin McKenna is an Observer columnist