Luxembourg and Andorra

Andorra is not that easy to get to unless you hire a car or go on a package tour including airport transfer. The main options are:

Bus from Barcelona: about three hours, ten or so journeys per day.

Bus from L'Hospitalet railway station in France (long slow journey from Toulouse): very limited service, one early morning bus and one late evening bus in each direction, primarily connecting with the through sleeper trains from Paris.

If you are entering Spain or southern France by air, this company seems to offer limited bus services from Barcelona, Toulouse and Girona airports (click on the Union Jack for English page but the Spanish is pretty easy to understand).

In Luxemburg, I'd say you could try and stay in Ettelbruck. It's a nice village right in the center of the Duchy which makes it a convenient base to visit the Duchy and to commute to Luxemburg city (about 30km). One very nice area of the Duchy is the Mullerthal natural park if you like hiking - it's also called Luxembourg's Little Switzerland.
Very near the German border, one really lovely little city that is a must see is called Echternach. That would also be a nice location, but not as central as Ettelbruck.

On a road trip through France one year, we stayed overnight in l'Hospitalet and in the morning drove to Andorra, just for a lark. It seemed nothing more than a giant discount shopping mall. We had a not very good lunch and left, never to return. The hotel in l'Hospitalet was great, though, and the dinner, cooked by the owner's grannie, was simple & delicious.

Similar to Norma's experience, we found that Andorra reminded us of one big Duty Free store and I wouldn't necessarily recommend going out of your way to stop in.