An absolute must see in Luxembourg are the various castles. Go and see the Grand Dukes Palace in the city center. The Royal family lives there most of the year and only opens up their home, the first two floors that is, during the summer months.
I'd like to highlight the one in Vianden which is situated in the north-east of the state of Luxembourg; about an hour's drive away from the capital. Do take the country roads Breezing along on a beautiful day in our convertible was such fun!
A cute little town with less than 2,000 people, it has a magnificent "working" castle; not just a ruin.
Set on a rock promontory, its history dates back to the 10th century combining several architectural styles: Romanesque and Gothic. The history of it is too complex to be described here. If interested, look it up on Wikipedia.https://en.wikipedia.org/wiki/Vianden_Castle. In short, it was damaged over the centuries and almost destroyed in the Second World War only to be restored in the seventies.
It is a fun place to visit, especially for children. By working castle I mean not only can it be toured but you can also see actors in historical gear parading the grounds and enacting "battles". It sits on top of a hill and then it is still a steep climb up to the castle itself.