When I was in Luxembourg, I really took my time (2 weeks) to go trough the country. And the most amazing city that I visited was Vianden. It was amazing to look at, it was really quite a walk to the city castle, but my hostel was really near the castle, so the views from my room were amazing. I really liked old people here, they had so much stories to tell. They were full of history and tradition. I also love food here. It was quite expensive (since it is quite a turistical city), but money was well spent. The castle itself was amazing too. So if you have time, and are thinking of going to Luxembourg, you should totally visit Vianden.