You will pay a premium for car rental when you pick up in one country and return in another. Consider trains.

You will be too late in the year to see the tulips in Amsterdam, but there are plenty of other things to see, even if you forgo their outstanding museums. We particularly liked time in Haarlem, a nearby university town. You don’t need a car in Amsterdam; parking is a hassle. All the natives ride bicycles. Nearby Hague is nice, but again mostly for the museums. Bruges is nice, but often crowded. Many think the beer in Belgium is the best in the world; my vote goes to the Trappist Ales. Nearby Brussels is large, but around the grand place is pretty scenic. Again, driving in Brussels is a hassle. Reims is nice, and is one place we needed a car, as we were staying at a gite, and getting information on public transportation is hard unless you are fluent in French. They have hot air balloon rides in Reims, but they are expensive and subject to the weather; in the week we were there, the weather looked good to me, but the pilot kept cancelling. Between Brussels and Reims is the Ardennes forest, and there is a lot of scenery and history there; you would need a car to see it. I would return the car in Reims and take the train to Paris.

I agree with Cleve that you might find the train faster, cheaper, more convent and even possibly more flexible, but since you’re a tripper, you know what you want — If you want to drive, go for it.

We enjoyed the WWII history at Bastogne. You could spend part of a day there, head on to Luxembourg City and then head on to Paris, stopping at Reims. The museum at the Bastogne memorial is small. Luxembourg City is a nice place to wander around — no flash and few tourists at either place and a relatively cheap place to sleep and eat for this part of Europe. Countryside would be a very pleasant drive, but no jaw dropping scenery.