If ever I am still in Luxembourg (looks like I go back to my Canadian east coast till I know if the UNESCO project works, in which case I am not sure where I'll land up) I could for sure join you to Amsterdam, I've been there a little week 3 years ago, it is really a cool and nice city to walk around. You can visit the Heineken brewery for one, there is an interesting clock factory a bit outside the city, that's not bad at all, you can visit the house of Anne Frank (history wise it's nice to see where it was, however, don't expect nothing spectacular), the history museum is nice and shows the urban evolution of the city. If like Bilbo, you're obsessed with jews, there is the jewish museum too (haven't been to that one). I recommand to rent a bike and to tour the city by night, Sarah will love it, many nice buildings to take in picture by night.

As for PAris... there is so much to see in there, I am not sure where to start with.