In Belgium you'll want to visit Bruges and Ghent and probably Brussels. Bruges because of the town itself (although its museum is also interesting); Ghent has a nice decorative arts museum and a folk art museum, a castle and an old part of the town; and Brussels has the early seventeen hundreds Grand'Place and the Horta Msuem plus more Art Nouveau sights including a music museum in a former Art Nouveau department store.

http://www.flickr.com/photos/mksfca/sets/72157622960079007/

http://www.flickr.com/photos/mksfca/sets/72157622960216715/

Or from Luxembourg you could head down the gorgeous gorgeous Mosel River Valley to the Rhine River and then head up thru Germany via Cologne to Amsterdam - by car the Mosel is really sweet - the Mosel runs a sinuous course thru a valley so sttep that it goes up several hundred feet quickly on each side - at many place lovingly covered with vineyards and dotted by cute small wine villages - even if you do not drink you may get intoxicated by the views - Trier is a historic city - one of the very oldest in Germany - dating back to Roman times and has several Roman relics like the Porta Negra, a huge gate that was once entryway to the Eastern Holy Roman Empire - Trier being the capital of the Western part - an old Roman temple is now the town's gaping Catholic basilica, etc.

Cologne is noted for its world-famous huge Gothic cathedral.

You could also tour the best of the Rhine - the fabled Rhine gorge between Koblenz and Rudesheim - by car or by frequent boats.

Cologne to Amsterdam is a short enough drive or few-hour train ride. So besides Belgium, consider going via Germany as well.

Thanks you both for your thoughts. Michael, thank you for the pictures. PalenQ, that is an option I hadn't considered. I will look into that as well as a possibility. There are so many possibilities it can be a bit overwhelming.

If you have the time, definitely stop in Brussels. It's a small enough city to see lots in 1-2 days and it's pretty easy to get around.
For art and museums, I would visit the Magritte Museum, take a Horta architecture tour or go to the underground Coudenberg palace ruins. See more on the Coudenberg here - http://bestofbrusselsblog.com/2011/10/03/night-at-the-museum/ There are tons of small art galleries in Brussels - check out the Rue Dansaert / Rue Flandre area, which also has lots of trendy boutiques, shops and bars.

Brussels is great for jazz. There are a few good clubs, including the Music Village - http://www.themusicvillage.com/

If you just want to walk around, the Sablon square is lovely and is where you can find lots of antique and chocolate shops. See more here - http://bestofbrusselsblog.com/2011/12/06/a-walk-with-friends/

Brussels also has some great restaurants. See my top picks here - http://bestofbrusselsblog.com/category/food-drink/. And of course you need to try fries (frites) from the country where they were invented. There are lots of frites stands but some are better than others - http://bestofbrusselsblog.com/2011/11/03/les-french-fries-2/

Sorry for the late reply, Jane. Thank you very much for the thoughts and links!

I may wind up having to fly in and out of Luxembourg rather than departing from a different airport as I had initially considered. If I have about a week, is there a good loop tour that I could consider?

From Luxembourg you could drive along the small towns in the Belgian Ardennes all the way to Brugge (or Gent, or Antwerp). The scenery is beautiful, the towns are very typical and very different from those in the northern part of Belgium where the art cities are (Brugge, Gent, Antwerpen). The Ardennes is the hilly part of Belgium whereas the northern part is flat. The Ardennes also have a large number of castles and ruins.
You will need a car to explore the real Ardennes as public transportation only serves the main cities.

Make sure to visit Dinant, the birth place of Adolphe Sax, and visit the Adolphe Sax Museum. And the Citadel, of course.

Other pretty, typical Ardennais towns are Durbuy (smallest town in the world), La Roche en Ardenne, Bastogne, Spa.

Also very typical for the area are the Coo Waterfalls, and the caves in Hotton and Han. The latter can be visited with a guide.

You could fly out from Brussels.

No worries about chocolate: there's chocolate all over Belgium!

Here's a link to the castles (unfortunately only in Dutch): http://www.wegwijs-ardennen.nl/kastelen.htm
And the caves: http://www.belgie.nl/informatie/natuur/grotten
Pictues of La Roche: http://www.la-roche-tourisme.com/nl_foto.php?variable=accueil|Foto|Ontvangst|nl

And a possible itinerary: Luxembourg / Arlon / Bastogne / La Roche / Han-sur-Lesse (caves) / Dinant / Namur. You could do this in 2/3 days, then drive to Gent/Brugge/Antwerp, drop off the car and continue your trip by train. Once in northern Belgium you can easily base in one place (Gent would be the most central) to see both Brugge, Gent, Antwerpen and Brussels.

If you need more information (or translations, 'cause most of the information is in Dutch or French), I will gladly help you. I'm a local from the Antwerp area.

Lux, Trier, Mosel, up the Rhine Cologne, Ghent, Brugge, Arras, Rheims (for the Cathedral, the walls and the forum), Charleville Meziers, Lux

Myriam, thank you so much for the detailed information! We are going to be doing some more research and I will certainly let you know if I have more questions.

bilbo, thank you also for your thought on a loop. Greatly appreciated!

After all of my planning and everyone's help, I unfortunately learned I will no longer have the time I expected to tour Belgium It looks like I will now have only one day to visit after spending a few days in Luxembourg for business and I must fly home from Lux. Assuming I can see Luxembourg during my off hours on my business days and have one day to take a day trip, where would be a nice place(s) to spend my free day? Note that I will not have a car.

I will file all of the other information away and plan to come back for a real visit in the future.

Catch the bus from Lux to Trier. Through great vinyards and you see an early part of the Mosel.

You could also hire a bike from Trier station and pop down the mosel coming back by train. If that interests, drop me note and I'll send you links

Alt hire a bike in Lux and peddle to Trier (coming back up is a little harder)

I have biked up the Mosel Valley umpteen times and IMO it is one of the very best biking venues in all of Europe - a deep often vineyard-carpeted gorge dotted by cutesy wine villages - nice bike paths hug the river the whole way. As bilboburgler sagely suggests - bike down the valley and return by train - I think if you rent a bike at the Trier train station you can return it to the Cochem train station but you can also put bikes on those trains without problem in baggage cars though there is a fee for that I believe.

If hurting for time the best - most gorgeous part of the Mosel Valley IMO is between Bernkastel-Kues and Cochem - you can take the train/bus to Bernkastel.

http://www.mybikeguide.co.uk/Mosel_Guide.php

stupid me there is a train as well taking roughly 50 mins Lux to Trier. There is good eating around the station. Also all the buses come in here and you can catch a bus to Olewig where the city vinyards are. If you go on the city website www.trier.de they can book you a very cheap tour of a local vinyard up on the hills, the local producers take turns at tuoring the visitors. If you can get Peter Terges who is crazy, speaks only German (though his wife is able to speak English) but knows so much about wine it makes a perfect trip to Europe.

Thank you bilbo and PalenQ. I was feeling a bit sorry that my plans changed so suddenly. But with your help I'm now feeling more optimistic that I can have a nice, albeit brief, experience even though my time was cut short. I'm sure having just a taste of the area will be better than nothing and will no doubt motivate planning for another trip when I have the luxury of more time and freedom.
Many thanks.