This tip is unnecessary for female VT's, because I think every true woman will find her way thru on this one :-)
Luxembourg City's principal shopping areas comprise the Grande Rue and its side streets, the Gare (train station) area, and the Auchan shopping center on Kirchberg. Jewelry and designer fashions are particularly well represented. Luxembourg chocolates, called knippercher, are popular purchases at the best pastry shops.
NOTE: if you are from eastern countries (read: poor countries), Lux may be a little expencive. But, you only live once!
The souvenir shops just near the Grand Ducal Place are the cheapest ones.
I checked all the other in the area.Also in the shops you can find little statuettes which are really cute.