My best friend lived in Luxembourg for a year and a half, and I went over to visit him on three occasions: in October 2013, April 2014 & November 2014.
There is a municipal lift that takes you from the upper levels to the lower levels. This is necessary because of the rocky promontories on which the city was built. We found it rather hard to track down, but got there in the end.
The grandest building in Luxembourg is the Notre-Dame Cathedral, which is just impossible to photograph in its entirety because of the number of large buildings that have since sprung up around it.
On my second visit we went to Fort Thüngen, which is pretty much a reconstruction. The original fort was destroyed after the 1867 Treaty of London, which required Luxembourg’s fortifications to be torn down. Across the valley you can see the Bock casements. These were tunnels built into the cliff by the Austrians, with openings every so often for cannon emplacements.
On my final trip we had a good old fashioned WHS drinking session on the cobbled streets of Luxembourg’s Grund area. A highlight of the city is the Luxembourg National Museum of History and Art. The next morning we took a train out into the countryside with the intent being to visit Vianden Castle (on the Luxembourg T-list), close to the German border.