6 days in the Netherlands, where to go and what to see?

As per the subject. Going with Mrs r77, we’re arriving in Eindhoven and going to Baarle-Nassau the next day, from there not decided yet. We’ll probably spend two days in Amsterdam but don’t mind hopping around the country (I’m thinking Utrecht, Groningen maybe? She’s into famous landmarks (canals, windmills, tulips), I’m into offbeat and castles, so there will need to be some compromises to be negotiated. No car, public transportation only.

Ideas and suggestions welcome, thanks.