Lakes, saunas, art, food – and Hamlet’s castle. A whistlestop tour of the best that Denmark has to offer

Don’t make small talk with strangers. Or talk about the weather. Or even ask people you know how they are… I read these social etiquette tips in a Denmark travel guide – four days into a 10-day trip. I’d already blown it on day one. “Look at that!” I said to the couple opposite me in the hotel’s below-ground sauna. A window looked on to the deep end of the outdoor pool. “A human fish!” Neither replied.

But there is so much to talk about, starting with our hotel, the Bryggen Guldsmeden Eco Resort, a former shoe factory in Copenhagen’s harbour-front neighbourhood of Islands Brygge. In the reception area there are trees (fake, tasteful) of pink blossom, deer heads (also fake), wicker hanging chairs, funky stained glass – and that sauna. And then there are the Balinese bedrooms, chic pool loungers, the Babette’s Feast of a breakfast, and the silver bullet Airstream serving drinks by the pool.