When there is a morning of working week Luxembourgoises don't like bus number 18 because it is always crowded and there is a Babylon of speeches inside. Yes, officials working in European Institutions are going to work. At the bus stop there is a flow of people who hurry to Commission, Court of Justice, Parliament or Court of Auditors. If you take a bus trip around you will see that all those buildings are nothing special from outside. And believe me that from inside it is the same :)
The city hostel (at the far right on the photo) overlooks the garden that belongs to the hospice opposite it. I don't know if you can visit it, I never saw anyone walking in it. But if you sit on the terrace of the hostel restaurant, it's very enjoyable to see.
Walferdange is not a very well-known place, it's a little village close to Luxembourg-city (15 min. by train) where there is nothing to see except the inhabitants and a few cows :-)
But there is one great thing that you can do there : enjoy the "Pidal Club". This is a big complex where you can go swimming, do some fitness, eat and most of all, relax in one of the many saunas, hammams and jacuzzis. My favorite place there was the bio sauna with fragrances and changing lights. Hmmm ! I also liked the traditionnal Finnish sauna and the swimming-pool outside. It was funny to run around naked outside while it was freezing (it was in january) ;-)
It's a great plan if you spend a few days in Luxembourg during winter. I know nothing more relaxing than that. And the price is quite reasonnable (about 16 €/day)