Refshaleøen is the post-industrial island. The B&W shipyard built ships here for nearly 150 years and closed in 1996; the island sat half-empty for two decades and is now what post-industrial Copenhagen looks like — Reffen (street-food market), CopenHill (the ski slope on an incinerator), La Banchina (swim and restaurant on the water), and the houseboats moored along the southern shore.
Four kilometres on the island, a hundred minutes with the climb. The 9A bus or — better — the yellow harbour ferry from Nyhavn drops you at the southern entrance; walk north up Refshalevej. CopenHill (officially Amager Bakke) is the BIG-designed waste-to-energy plant with the dry-ski slope on the roof and the eighty-five-metre climbing wall on the side. Climb the hiking trail to the top; ski down if you've brought a season pass.
Reffen is the converted shipyard street-food market, summer-heavy, dozens of stalls in the old workshop buildings. La Banchina is the New Nordic swim spot — tiny restaurant, wood-fired sauna, harbour ladder. Walk back south for the boats and the ferry to Nyhavn — the view across the harbour to the city is the closing payoff.