Zealand

Castle

Best known as the Elsinore Castle of Shakespeare's Hamlet, this Unesco World Heritage Site is a vast Renaissance masterpiece topped by baroque green-copper spires. It's ringed by moats, fortifications and powerful Vaubanesque star bastions that you can discover without a ticket. But it's well worth the entry fee to explore the inner palace's rooms, tapestries, ceiling paintings and viewpoints and, best of all, to delve into the spooky maze of casemates – subterranean dungeon passages barely lit by flickering paraffin lamps.

Castle

One of Denmark's most impressive buildings, this gigantic, Dutch Renaissance–styled fortress-palace rises proudly out of photogenic moat-lake Slotsø. Access is free to the impressive central courtyards and huge, beautifully tended park with baroque gardens. To visit the interiors (ticket required) you'll need around three hours to do justice to the 80-plus rooms overloaded with beautiful furniture, tapestries, endless portraiture and gilded decor of astonishingly pompous grandiosity. Copious info-cards, along with free audio guides in nine languages, add plentiful context.

Museum

Ingeniously built into a dry dock beside Kronborg Slot, this subterranean museum merits a visit as much for its design as for its informative multimedia galleries. These explore Denmark's maritime history and culture in dynamic, contemporary ways. Alongside nautical instruments, sea charts and wartime objects, exhibitions explore themes including the representation of sailors in popular culture, trade and exploitation in Denmark's overseas colonies, and the globe-crossing journeys of modern shipping containers.

Museum

This extraordinary museum of modern and contemporary art should be high on your 'to do' list even if you're not normally a gallery-goer. Along with its ever-changing, cutting-edge exhibitions, much of the thrill here is the glorious presentation. A maze-like web of halls and glass corridors weaves through rolling gardens in which magnificent trees, lawns, a lake and a beach view set off monumental abstract sculptures (Henry Moore, Jean Arp, Max Ernst, Barbara Hepworth etc), making them feel like discovered totems.

Museum

Five original Viking ships, discovered at the bottom of Roskilde Fjord, are displayed in the main hall of this must-see museum. A short walk away, the same ticket gives access to the workshops of Museumsø, where archaeological and reconstruction work takes place, and Nordic longboats depart. There are free daily guided tours (45 minutes) in English in the summer; see the website for times.

Cathedral

The crème de la crème of Danish cathedrals, this twin-spired giant was started by Bishop Absalon in 1170, but has been rebuilt and tweaked so many times that it’s now a superb showcase of 850 years’ worth of Danish architecture. As the royal mausoleum, it contains the crypts of 37 Danish kings and queens and is now a Unesco World Heritage Site. The entry fee includes a comprehensive, full-colour 48-page guidebook.

Museum

Within a startling architectural statement of a building, this spirit-lifting, highly interactive museum delivers a multisensory, experiential and often humorous journey through the evolution of rock music and youth culture from the 1950s to the present. Walls of headphones let you listen to music time capsules, and spin-to-hear turntables explain about gramophones. Play with interactive musical lights, learn why toilets were integral to Danish music production and practise various dance steps on the hot-spot stage beside the 'world's biggest mirror ball'.

Archaeological Site

This new centre provides access to the world's richest Viking gold-find site, at what was an important ritual centre a millennium ago. Of course the Viking-era wooden buildings are long gone, their outlines marked by granite slabs, but the visitor centre has a beautiful reconstruction of the 1.8kg Tissø woven-gold neck-ring found here along with 12,000 other artefact fragments. Kids can play paint-and-sacrifice or dress up as Vikings, while an English guide-text gives context to the era's religious beliefs.

Bridge

Some 18km long and incorporating a suspension bridge that's arguably as elegant as the Golden Gate, the Storebælt link is a remarkable piece of engineering linking Funen and Zealand on what has been dubbed Denmark's biggest man-made structure.