I'm glad you're visiting Luxembourg! We were there last fall and loved it. It's a beautiful, friendly, clean little country. Lots of English speakers. And an amazing public transportation system. For 4 euros per person per day, you get unlimited travel on trains and buses throughout Luxembourg. So since you are wanting to use trains or buses, I would suggest that you base yourselves not in Luxembourg City, but in Ettelbruck.
Ettelbruck is a main transportation hub located in the central part of the country. We stayed in nearby Diekirch last fall, using public transportation, and every trip we took went through Ettelbruck! It didn't take us long to figure out that this is where we should have stayed. Since Luxembourg is so small, you can easily take a day trip into Luxembourg City (maybe 1 hour on the train) to see the sights, but return to Ettlebruck for the small-town ambience (and much lower prices).
Ettelbruck is a charming little city of about 7,000 people, and an important WWII site. General Patton led the final liberation of Ettelbruck from the Nazis in 1944, and there's a major square in town called Patton Square, and also a Patton museum. There's a market downtown on Friday morning, so if you like small-town market days, you might want to schedule yourself there on a Friday. The central square (pedestrian only) has several good restaurants, a good bakery, places to sit outside with a beer, and a great gelato shop. Since we didn't stay there, I have no hotel recommendation, but I suggest you find someplace near the train/bus/downtown area. Here's an email address for their tourist info office -- you might get some information from them: email@example.com.
Diekirch, where we based ourselves, has an amazing WWII museum that you don't want to miss. It's maybe 15 minutes from Ettelbruck. Allow several hours for the museum -- it's huge -- has actual tanks and vehicles used in WWII, plus dioramas with soldiers in actual uniforms, and room after room of artifacts. After the war, farmers living in the area collected the tanks, trucks, uniforms, etc. left behind, and stored them in their barns. At some point, they decided to gather them together in this museum. It's truly remarkable. Most interesting are the photos of soldiers who fought there, and letters they wrote after the war, describing their time in Luxembourg. There's an American flag flying outside of the museum and a large banner, "Welcome to our liberators." I have never felt more welcome in Europe as an American than I did in these little towns!
Another interesting thing to see in Luxembourg is the "Family of Man" photographic exhibit in Clervaux (a short train ride away). And there's a castle in Vianden that you can visit. You can easily fill 4 days in Luxembourg.
In Belgium, we stayed in Bruges and did the Flanders Field tour with Quasimodo Tours -- very highly recommended. We loved Bruges but that was the only war-related activity we did there ... lots of chocolate and beer, though. We started our trip in Bruges, took a train to Diekirch (changing in Ettelbruck, of course). From there, we went to the Rhine in Germany, for the annual Rhine in Flames, which will take place September 19 this year. A truly amazing sight, if you have a couple of days to spare. Here's a link.
Have fun planning!