Luxembourg itinerary

all buses, trams and trains in the entire country are indeed free to ride, and every town is reachable by bus (usually) or train.

Consider a side trip to the town of Vianden and its famous castle. https://en.wikipedia.org/wiki/Vianden Yes, you don't need a car. The wonderful Battle of the Bulge museum in Diekirch is also on a bus and train route.

In the Luxembourg City History museum, I particularly liked the displays that showed the city walls and layout at different times in history. There were additional artifacts telling the story of the city, too, but I like maps and models.

We also enjoyed Vianden castle. There are a lot of displays in the building next to the gift shop as well as some furnishings in the castle.

Day hikes / nature near Echternach might be fun. Very pretty area.

Two places not in Luxembourg but very close to it are Trier in Germany and Bastogne in Belgium.

To be fair, we had a car. I can't speak to transportation.

I found the American cemetery very much worth visiting as well as the museum mentioned by Nigel. It isn’t a large museum and we spent a couple hours there. Because we visited as part of a longer trip to a few countries, we had a rental car.

I’d agree with Nigel that the WWII museum in Diekirch is well worth a visit. You could easily spend half a day here.

We also enjoyed the castle in Vianden, and the Family of Man photographs now on permanent display in a chateau in Clervaux.

We used only public transportation. We stayed in Diekirch but wish we had based ourselves in charming Ettelbruck, which is a hub for the trains & buses. Never did get to Lux City.