Grand Ducal Palace
The Grand Duke of Luxembourg and his family have this lovely palace in the middle of the city. It's their official residence and where most of the the business of the state takes place. If it wasn't for the appropriately-stern guards in the booth and the iron fence with the ducal crest, I would not have guessed that this building housed the head of state of the country with the world's largest GDP per capita. It's a beautiful building, but not over-the-top and very approachable.
It does have quite a history. Built in 1572, it started out as a town hall. It served various governmental functions for three hundred years until the 1890s, when it was handed over for good to the Grand Duke and his family. But the building hit a low point 50 years later in the early 1940s, when the Nazi occupiers used it as a concert hall and tavern, destroying much of the art and interiors. When the Grand Duchess returned from exile in 1945, the buiding returned to the Grand Ducal seat, where it has remained uneventful for the last 60 years.
Luxembourg, February 2006.