A few months back the tourist information store (denhaag.com in English) moved from the ground floor of The Hague public library’s main branch to The Hague Central train station.
The tourist office now goes by the name “The Hague Info Store”. Oddly enough, they do also use (THIS) as an official acronym which I find a bit silly.
You can find the store around the corner from the playable piano. (Who knew there is a website which tracks publicly playable pianos throughout the world? See also pianos.pub/location/netherlands.)
They have a few Lego-like sets under the brand “Brickworld designs”.
The Hague specific souvenirs…
You can also have a look at their webshop (souvenirdenhaag.nl, available in Dutch).