Copenhagen's harbour is about to get a striking new landmark: Kai, a 5,800 square-metre public bathhouse designed by Japanese studio Kengo Kuma Associates, opens on Saturday 5 December after eight years in the making. The project was delayed from its original 2021 date by the pandemic, but the wait looks worth it.

The building packs in ten pools spread across several levels, including a 25-metre pool on the ground floor, an open-air rooftop pool and a heated onsen-style bath overlooking the water. There's year-round harbour access too, with designated swimming and dipping zones around a timber boardwalk. Winter swimmers needn't worry about the cold: the first-floor outdoor pools are warmed by a sustainable vertical ground-source heat pump system.

Here's the kicker for travellers: entry prices are expected to match Copenhagen's other city-run 'water culture houses', meaning under 100 Danish kroner – roughly £7.50. Capacity is capped at 380 swimmers, so quieter sessions are likely off-peak. The whole 989 million DKK (about £110 million) project was funded by the City of Copenhagen and Nordea Fonden, and it sprang from resident surveys calling for a central public pool.

The location is a win as well. Kai sits on Paper Island, directly across the harbour from Nyhavn and easily reached on foot or by bike via a bridge. The island, once home to a beloved food market, has been redeveloped with restaurants and cafes, and now links the old town with Holmen and the former shipyard area of Refshaleøen. It slots into a harbourfront already lined with architectural heavyweights like the Opera House and Royal Danish Playhouse.

Swimming is deeply woven into Copenhagen life – the city dropped floating pools into the harbour in the early 2000s after the shipbuilding industry collapsed, and winter bathing has since boomed as a wellness ritual. Clubs with sauna access are so popular they have long waiting lists, which is why Kai's affordable, bookable-without-membership model matters for visitors.

Want to extend the aquatic theme? Sandkaj in Nordhavn offers lane swimming straight in the harbour, with saunagus (a Danish sauna ritual) nearby at Saunanor. For something spa-like, Skodsborg Spa Hotel up the coast – a former sanatorium – has 16 bathing experiences and a private beach jetty. Valby's Water Culture House is another sleek municipal option with a slide and hot pools.

Pack the swimsuit. This one's an easy, cheap add-on to any Copenhagen city break.