A must see during your day out in The Hague is the Mauritshuis (House of Maurits). This museum is where you encounter Dutch masters like Rembrandt and Vermeer and the building itself has existed already since the 17th century and has recently gone through a 2 year renovation.
Build in the typical Dutch classical style, the experience of the building itself is already worth a trip. While the artistic value of the paintings is in no way below that of the Rijksmuseum in Amsterdam, the Mauritshuis allows you to explore them a lot more comfortable without the exceptional volume of visitors.
Directly next to the Mauritshuis in The Hague you also find the Binnenhof where you can get a glance of Dutch politics up close!