Denmark has several pretty parks in the city center, but the Botanical Garden is in a league of its own. It’s free to enter, and you can happily wander along pathways lined with rhododendrons, through alpine gardens, and around the lake. The star attractions are the huge greenhouses, inspired by London’s famous Crystal Palace, that date from 1874. The main building, called the Palm House, has a vertigo-inducing spiral staircase that leads to a walkway suspended inside the dome at the height of the canopy of the palms. It’s simply remarkable.