base for Utrecht, Den Bosch, The Hague, Leiden, Haarlem

Well if you want to see all of the ones you listed, and it’s a little unclear whether you do, I wouldn’t pick Utrecht as a base. As a destination, it works though, as you could easily get there from Amsterdam, Leiden or even The Hague without too much trouble.

But if it was me, I would go with Leiden just because I love Leiden and I think it would be wonderful to stay there. It’s much more residential than the other places around Amsterdam, is is very charming with a wonderful atmosphere, and it’s easy to get to and from by train.

Given its central location, Utrecht is a good bases to visit all the places you mention, including Paleis Het Loo.

I’m however a bit confused by your itinerary;
“ I'll begin in Amsterdam, then go west to visit Palais Het Lo.
After that...I need a convenient base or two for day-trips by train before heading back to Schiphol Airport.
With the remaining 5 nights, this is my unfiltered wish list:
Utrecht, The Hague, Den Bosch, Haarlem, Leiden”

What day trips do you want to make from the “convenient base or two”? And do then after that need a new base to see Utrecht, The Hague, Den Bosch and Leiden? I guess what confuses me is the phrase “remaining 5 nights”.
Can you please clarify your planned itinerary a bit more? It would also help to know what time of year you plan to be here.

There are still many castles with a moat in the Netherlands. Here an overview per province:

https://en.wikipedia.org/wiki/List_of_castles_in_the_Netherlands

The most famous are Muiderslot near Amsterdam and Loevestein near Gorinchem south of Utrecht. For the latter you have to take the foot ferry from Gorinchem to very charming Woudrichem with an additional ferry to the castle. Lovely places and setting, to my opinion good for a daytrip you are looking for.

https://muiderslot.nl/en/
https://www.slotloevestein.nl/en/

De Haar Castle west of Utrecht is open to public too, despite being a 19th century rebuilt worth a visit.

https://www.kasteeldehaar.nl/en/

It was my second time visiting the Netherlands that I stayed in Utrecht. From there I made a return visit for the day to Amsterdam, then a day trip to Den Haag, and then headed for Schipol from there as well.

I will disagree a bit with others, but Leiden would fit the bill as a base for all that you want to do. It is the most central to most of your wish list, only 15 to 20 minutes to Schiphol by direct train (better than Haarlem by train or bus), about a half hour into Amsterdam, a bit less to Haarlem, 15 minutes to The Hague, a few minutes more to Delft, 45 minutes to Utrecht, with Den Bosch the only outlier, but only 90 minutes away.

For visiting Palace ( Paleis in Dutch) Het Loo adjacent to Apeldoorn you can stay for instance in one of the charming Hanseatic cities like Deventer, Zutphen, Zwolle and Kampen along the IJssel river. Apeldoorn is 10 minutes by train from Deventer, Zutphen needs almost the same time.

For planning train journeys: https://www.ns.nl/en/journeyplanner/#/

Giethoorn takes for instance around 1h 40min with train and bus from Deventer. For planning public transport in general: https://9292.nl/en/

Visit Haarlem from Amsterdam.

Utrecht, Leiden or Delft would work for me as the second location.

Thanks to you all for the suggestions and questions. Early planning is never clear, so apologies for the lack of clarity.

One week is in Amsterdam, that is all set for the late fall. Leiden or Geithoorn will be a daytrip from Amsterdam.
The remaining week will be split between Utrecht and Haarlem, to enjoy them and the surroundings by train.

Hotel or restaurant suggestions for Utrecht and Haarlem would be welcome.

Thanks,
Lee

Some restaurant suggestions for Haarlem can be found in this thread: https://community.ricksteves.com/travel-forum/netherlands/itinerary-help-amsterdam-and-haarlem