Who says size is important? Take Aalborg. It may only be Denmark's fourth-largest city but it crams in more culture, good looks, fine food and cool shopping than anyone could expect for a town about the size of Bournemouth.

A waterside location on the Limfjord (think a wider version of the Thames rather than jaw-dropping Norwegian-style fjord) has shaped the flow of history across this North Jutland port, which in the 16th and 17th centuries rivalled Copenhagen, courtesy of the wealth from herring, glass-making, tobacco and spices.

For decades, Danes have seen Aalborg mainly as a jumping-off point for the dune-backed beaches that stretch in a sandy ribbon 100 miles up the Jutland coast from Hals (20 miles east of the city) to the picturesque 19th-century artists' colony at Skagen.

But Aalborg itself has found a new driving force in culture. This post-industrial transition is exemplified by Nordkraft, a former generating station that is in the process of turning into an artistic powerhouse (two theatre spaces are still to come). At present, Nordkraft is primarily a night-time venue, with arthouse flicks at the fabulous Biffen cinema or gigs at Skraaen. But the small Kunsthal Nord gallery on the first floor provides a rough-hewn daytime draw, its contemporary art framed by old brickwork and metal ducts.

Culinary pleasures are complementing cultural ones. Seafood, of course, is a familiar Danish delight – blue mussels, plaice, cod, salmon and herring – but Aalborg's chefs are also turning to the likes of wild boar from nearby forests, aged goat's cheeses from Nibe and mineral-rich sea salt from the island of Laesø.

Before lunch, we take in the waterfront homage to Aalborg's most famous modern son. Architect Jørn Utzon may be best known for designing the Sydney Opera House but the Utzon Center (utzoncenter.org) shows how the master learned his craft in Aalborg, taking inspiration from the curved hulls of the boats his father designed in the city's shipyards. The building, though, lacks the wow factor of Utzon's antipodean masterpiece, with its utilitarian steel rooftop curves and modest interior space geared to workshops rather than exhibitions. The view of the water from the cafe offers some compensation.

Wandering along the quay, we mull over options among Aalborg's restaurant boats. The musk ox and reindeer on the menu at the sturdy old ice-breaker Elbjørn (isbryderen-elbjoern.dk) are tempting, but as it's sunny we opt instead for a deck table and the laidback ambience of the converted houseboat Den Fede Aelling (denfedeaelling.dk). We tuck into plaice with lingonberries and capers, and the sun is warm and the beer cold as we watch the swing bridge rise and fall for yachts cruising out.

We set a course past the imposing 17th-century Aalborghus Castle into the old town, where pastel-hued period buildings now shelter shops mixing modern style with retro classics. Nørregade has some of the best, often tucked away in cobbled courtyards or on tiny side streets, such as the vintage hotspot Det Gyldne Dådyr or the Lange ceramics gallery, amid gorgeous period cottages on cobbled Hjelmerstald.

For dinner, we avoid the city's two most high-profile restaurants – the Michelin-noted Mortens Kro (mortenskro.com) and the 400-year-old Sohngårdsholm Slot (sohngaardsholmslot.dk). We're happy to find ourselves back bobbing on the fjord aboard Prinses Juliana (prinsesjuliana.dk). This 80-year-old Dutch vessel now hosts distinct dining spaces of varying swishness, though the food is excellent wherever you sit. We go for twilight upper-deck water views, accompanied by turbot with foie gras on a compote of apples and pears, and braised monkfish and lobster on pea purée with smoked almonds.

Back in town, 1000Fryd (1000fryd.dk) provides sharp post-dinner contrast. Hidden away on Kattesundet, this venerable old town hangout has dished up alternative Aalborg vibes for three decades, with a clientele as mixed as its busy gig list. But Monday is quiet, and we soak up the boho vibe in peace over a couple of organic beers.

The next morning, an amble through the tranquil Ansgar churchyard brings us to the sculpture-dotted Skovdalen and North Jutland's principal gallery, Kunsten (kunsten.dk). From its unflashy rectangular white exterior you'd never guess it was partly designed by Alvar Aalto, the Finnish "Father of Modernism"; he saved his genius for a light-flooded interior where intriguing modern Danish art vies for attention with gorgeous fixtures and fittings.

I've no idea who the architect of the Budolfi church was, but this is Aalborg's most outwardly beautiful building – a ravishing 14th-century affair on Algade (the main shopping street), mixing pale-walled serenity with painted wood panelling. The house of merchant Jens Bang is another eye-catcher, whose five storeys have commanded Nytorv square since the 1620s. It's privately owned so you can only admire its facade.

We have lunch a stone's throw away at Søgaards Bryghus on the restaurant-ringed CW Obels Plads (soegaardsbryghus.dk). Aalborg is famous for producing one of Denmark's premier aquavits (you can visit the riverside distillery – see aalborgakvavit.dk) but the superb Jutland beers made at Søgaards now provide a lip-smacking complement. They're a perfect match too for the plate of herring and delicious local mussels we share at the brewery restaurant.

Back by the water, the industrial tangle near the Ostre Haven conceals Platform 4 (platform4.dk), our final cultural stop off. Another post-industrial space, our visit finds local artists on show but its programme reveals upcoming events ranging from alt-cinema festivals to showcases of cool electronica.

So, a spectrum of arts, good nosh and Danish chic. If these are small-town charms, I'm all for them.

• Norwegian (020-8099 7254, norwegian.com) flies direct from Gatwick to Aalborg from £54 rtn inc tax. The Quality Hotel (+45 7012 5151, choice hotels.no) offers doubles from £92 B&B. Further information from Visit Aalborg (+45 9931 7500, visitaalborg.com)