Planted from 1871 to 1874 -- and still around to thrill us to this day -- these botanical gardens are on a lake that was once part of the city's defensive moat around Rosenborg Slot, which fronts the gardens. Greenhouses grow both tropical and subtropical plants, none finer than the Palm House, which appears even more exotic this far north. Retreat here on a rainy day and imagine you're in the tropics. An alpine garden also contains mountain plants from all over the world.