One of the first places to visit in Luxembourg has to be the Cathedral of Santa Maria and the Cathedral of Our Lady, a Gothic cathedral with some Renaissance elements to its architecture. Also important is Fort Thüngen, one of the most important historical military Luxembourg attractions, located in the park around Dräi Eechelen. The complex was built in 1732 and has been called "Three Acorns" because of its shape. Not sure exactly what to do in Luxembourg but interested in museums? There are two important museums here found inside the fort -- the Grand Duke Jean Museum of Modern Art and MUDAM, the modern art museum. The fort, with the rest of the Middle Ages era fortifications in the city, was declared a World Heritage Site by UNESCO in 1994.
Grand Ducal Palace is another one of the things to see in Luxembourg. It is the official residence of the Grand Duke of Luxembourg. Here he performs most of his duties as head of state of the Grand Duchy. Besides this, visiting the city council and the National Museum of History and Art are essential Luxembourg activities. The city is also characterized by a rich wealth of museums. As well as those already mentioned, you'll find attrations in Luxembourg like the Luxembourg Museum, the Villa Vauban art galleries and the Casino.
And that's just a taste of all the stuff to do in Luxembourg. Check out what minube users have to say about their experiences in the city for even more things to do in Luxembourg.