Hello,
We will be visiting friends in the Hague in April of 2022 for 4 days. We have an additional 4 days to travel elsewhere and are leaning towards Northern Germany. We are flying into Amsterdam, but are open to flying out of another city. I prefer not to have a car, and we have two teenaged sons. Thinking Cologne, a day trip on the Rhine, a castle visit? Any World War II sites doable?
Just getting started, and I appreciate any suggestions. Thank you!

Arnhem might interest

I'd prefer to look at say the Mosel, you start with Trier which has Roman remains and as you progress down the valley you'll find castles and stuff until you join the Rhine at Deutches Eck across from here, by cable car, is a fortress (1890s??) so lots of things to see.

If instead you go North you might like Hamburg and the submarine sheds to the west.

Cologne is easy by ICE, So is Dusseldorf. Hamburg is quite a train journey, and so is Trier. You might be interested in Maastricht and Aachen?

But the bits of Germany that are easy to access are all rebuilt since the war, nothing wrong with that but they wanted to see WW2 memory stuff.

Cologne is one big WW2 memory site, but you need to know where to look. The entire Ruhr area is, in fact, and I would very much recommend Arnhem (and Nijmegen)

The Rhine is very easy access from the Netherlands. There are 4 rail corridors from the Netherlands into Germany: roughly Eindhoven - Mönchen-Gladbach - Köln (Cologne); Arnhem - Duisburg - Düsseldorf - Köln; Hengelo- Rheine - Osnabrück and Groningen - Leer- Oldenburg - Bremen. I have done the reverse trip a couple of times on different routes and I personally really like the Bremen - Groningen route myself. I have also done this by car. It is a long way up to Groningen from Amsterdam so it's quite time-consuming. If you have a car you can drive up across the Afsluitdijk, which is quite an event in itself, and Friesland (for instance, Leeuwarden) is interesting, quite a different side to the Netherlands. However, if your interest is WWII I would probably just stick to Arnhem and on to the Ruhrgebiet. It was an area that was very heavily bombed during the war and even now, Cologne is not what you'd call a pretty city in terms of architecture because it was hastily rebuilt for purpose and not effect. However the cathedral is one of those iconic sites that should not be missed. You might be interested in the site of the Ludendorff Bridge (the bridge at Remagen, near Bonn), which was never rebuilt. There is a famous Hollywood film about it. There are of course other things to interest you along the Rhine, it's a very strong tourist magnet.

Lavandula

Leer - Oldenburg - Bremen is not really a viable connection for most travellers imo, you need to get to Groningen to make use of it and it's not that frequent.
The specs were: no car.
Arnhem = Market Garden and Operation Pegasus ( A Bridge Too Far)
Also in Cologne: the Römisch-Germanisches Museum, bc Cologne was an important trading city on the Rhine in Roman times.

If a car were an option I would suggest Overloon museum and Margraten American Cemetery

https://www.oorlogsmuseum.nl/en/

https://www.abmc.gov/Netherlands

You stay in Maastricht, and find some nice walks in the Limburg hills, or visit the drielandenpunt (three country point) for instance.