Probably the thing I found most interesting about Amsterdam was it was the only place in the world I’ve ever seen dedicated traffic lanes for five distinct modes of transportation on one single street—pedestrians, bicycles, cars, trains, and boats.
I wonder whether that might explain a number of incidents where I've been treated very very rudely when I've visited Amsterdam or Rotterdam, even when I'm not "one of those toursists".
Rotterdam, The Hague, Haarlem, Leiden, Delft, Gouda, Utrecht, Zaandam, maybe even Alphen aan den Rijn. I’d even consider Groningen on this list (although Groningen is a 2 hour journey).
These are all places within approximately an hour or less by train of Amsterdam’s central station, that have fantastic culture (lots of art, history, and other museums), and are (mostly) classic old Dutch cities.
Don’t get me wrong, Amsterdam has some nice museums that I also go to occasionally too, but if you want to go and see Dutch things that are just as nice without the crowds, you can go almost anywhere else.