Family trip to Belgium-ish

Luxembourg (the country) is full to the brim with great walking and hiking. Luxembourg (the city) has very different architecture and topography, and very scenic.

and all public transportation, trains, buses (many very comfortable) and trams, in the whole country is completely free to all.

Luxembourg is adjacent to Belgium, Germany and France. The Moselle (Mosel) river valley is beyond beautiful with vineyards and castles.

If you do go to Bruges, you can make a day trip by train to Ostend and visit the Atlantic Wall Museum. We followed that up with a visit to DeHaan and walk on the (chilly and windy) beach. Further along the coast there is an aquarium, which we did not visit. We were there in late September, so maybe a little warmer than April, but it wasn't beach weather. We put our toes in the North Sea so we could say we had.

6-8 days starting in Frankfurt is not much time for Belgium, seeing that you are talking a half day to get there, and another half day back, being there the night before your flight out.

But, if I were doing it, I would hop the first train to Ghent. Centrally located, you can easily daytrip to Brussels, Bruges, and Antwerp. You can also do any amount of biking and hiking along canals.

A second option, might be someplace like Koblenz. Not too far from Frankfurt, but easy access to the Rhine, the Mosel Valley, the Spa town of Bad Ems, with Cologne not too far.

Science / history museums in the Netherlands and Belgium are:

Nemo in Amsterdam: The largest science museum in the Netherlands, for all ages.
https://www.nemosciencemuseum.nl/en/

Naturalis Biodiversity Center and Rijksmuseum Boerhaave, both in Leiden. The latter with a lot of historical scientific instruments, like some of the earliest microscopes.
https://www.naturalis.nl/en
https://rijksmuseumboerhaave.nl/english/

Ghent University Museum and more for the kids: Technopolis in Mechelen. Mechelen has also a lovely historical city center to visit. You can climb the bell tower of the cathedral there for a magnificent view. There is a brewery too open to public. https://www.technopolis.be/en/
https://www.hetanker.be/en
https://www.gum.gent/en

If the Roman period is of interest, the Gallo-Roman Museum in Tongeren, topnotch and really off the beaten path. https://galloromeinsmuseum.be/en/

In Antwerp Museum Plantin-Moretus, a huge 16th century printing office and inscribed in the UNESCO World Heritage List.
https://museumplantinmoretus.be/en/content/welcome-museum-plantin-moretus

Open air museums in both countries:

Like the Zuiderzeemuseum in Enkhuizen north of Amsterdam and Bokrijk having it’s own train stop, halfway between Hasselt and Genk east of Antwerp. https://www.zuiderzeemuseum.nl/?lang=en
https://bokrijk.be/nl

From Bruges popular is biking along the canal to Bruges and even further Sluis in the Netherlands. Albert Einstein stayed a half year in De Haan before finally moving to Princeton. His temporarily home is still there, however only to see from the outside.

Theme park De Efteling and both south of Frankfurt: Technik Museum Speyer and the one in Sinsheim.
https://www.efteling.com/en
https://sinsheim.technik-museum.de/en/

Thank you all for your suggestions! You've given me lots to explore and I appreciate all the input.