cities other than Amsterdam

I think you will like the Kröller-Müller Museum; an art museum located in the Veluwe national park. See their website: https://krollermuller.nl/visit and the national park's website: https://www.hogeveluwe.nl/en .

In what season are you planning to visit the Netherlands?

You should definitively consider the Kroller-Muller museum and Hoge Veluwe. Stay in Arnhem (year-round) or in one of the towns in the vicinity of the park (late March-early October)

If you like the countryside, you might also like the smaller 'Hanse' cities ( https://en.wikipedia.org/wiki/Hanseatic_League ) such as Zwolle, Deventer and Zutphen. Personally, I think Zwolle has a charming city center, but there are not nearly as much tourist attractions in these areas, compared to the major cities.

I would recommend staying in Utrecht or Arnhem and traveling daytrips by train from there. If the weather is nice, you could rent a bike near the Veluwe national parks. Plan your journeys through ns.nl/en and 9292.nl/en and use Google Maps for cycling routes, although those can't always be fully trusted.

cycle routes can be planned using https://en.routeplanner.fietsersbond.nl/

Utrecht would be a perfect base. Interesting city. Good facilities. And right in the middle of the country from where you can do a lot of worthwhile day trips. Zwolle (and nearby Kampen) is less than one hour away. The wonderfully preserved fortified town of Naarden is a 20-min walk from the station Naarden-Bussum (30 mins from Utrecht). A mere 10 mins from the station Hollandsche Rading for a walk in the woods. And it's half an hour from Schiphol airport with a direct train, leaving every 15 mins.

Having a week I would do a tour with a car around the IJsselmeer. Going clockwise you can start with places like Hoorn and Enkhuizen. Further driving over the “Afsluitdijk” to much overlooked Friesland, one of the most beautiful provinces of the Netherlands with lovely countryside and little towns like Sloten and Hindeloopen to name a few.

You can indeed visit the already named Hanseatic towns along the river IJssel and include a detour to Lelystad for going to the Batavia shipyard where you can see rebuilding a 17th century warship and another finished. Not too far from Kröller-Müller is former Royal Palace Het Loo near Apeldoorn.

If having enough time you can add the Deltaworks in the southwestern corner of the Netherlands, with not to miss the Eastern Scheldt Storm Surge Barrier and the Maeslant Barrier.

For accommodation check out the following sites;
www.erfgoedlogies.nl and www.bijzonderplekje.nl
I agree that the area around Apeldoorn is truly amazing. The Kroller Muller is a must. Close by, in Gorssel is Museum More. The area is pitoresque. Then you must visit Zwolle. World renowed for its 3 michelin star restaurant De Librije. It also boosts a wonderful museum, De Fundatie. This museum has a dependance in the country side, Castle Nijenhuis.Dont forget the North. Het Drents Museum in Assen ahs some wonderful exhibitions and so does Het Gronings Museum in Groningen. The islands in the north are also worthwhile. You can even island hop.

Among a number of places we visited, we enjoyed Harlingen, Zaandam, Kinderdijk, Schoonhoven and Giethoorn. If you like castles, there's a nice one in Hoensbroek.

We enjoyed beautiful Leiden for a week and took day trips by train to The Hague, Rotterdam and Kinderdijk, Delft, Amsterdam.

Schoonhoven is indeed a nice town . It is well known for its beautiful silverwork that's made there .This is in the " Bible Belt " so on Sunday everything is closed .