Luxemburg and its old town, a UNESCO heritage site, has ruins of the castle from 963 which can still be seen. It is a town with a lot of juxtaposition of old and new. If you visit Place d'Armes a large square you'll find that it is surrounded by lots of restaurants and cafes and perfect for people watching. Luxemburg is a relaxing city as there are lots of historical sights within easy walking distance.
At night, there are good opportunities to get images of lights reflecting from the The Cathedral of Notre Dame whichholds the tomb of a 14th century Count of Luxembourg.
Built between 1572-74 to serve as the City Hall, the Renaissance style building near Place d'Armes has been the Grand Ducal Palace since 1890. It is sometimes open for tours but best to check dates and times at the Tourist Information Centre.
Here some impressions of the town.