You have an excellent suggestion. I suggest that you use the DB (or NMBS) website to research some of your planned daytrips, because they may take longer than you would like them to by train. I never "advocate" renting a car in this area, but we did have a car for eastern Belgium once. We stayed in a slightly faded rural resort in Lanaken, for easy car daytrips, instead of in a city.
After reading the link below, you might want to add a night in Cologne, and maybe hit Dusseldorf or (smaller) Monschau. Depending on your Belgium routing, you might consider the Bokrijk Open Air museum, which has its own train station. I would caution you that some of the cities with lovely old-town sections (like Tongeren and Diest) for example, have very small (if lovely) old areas, surrounded by banal postwar low-rise masonry cities. I'm not bad-mouthing them, I'm just talking about targets for a long train trip, versus having a car.
When your train stops in Liege, step down to the platform briefly (but not away from the train!!) to view Francisco Calatrava's famous train shed. This gives an idea of what his building at the NYC World Trade Center area was supposed to evoke, but was "value engineered" out of the project.
https://community.ricksteves.com/travel-forum/germany/can-i-see-enough-of-cologne
