The building seems to be an ode to 'Fondation Beyeler' and the garden is by the great Piet Oudolf. You can walk around the estate even if you don't want to enter the museum. 

Great exhibition space for contemporary art.

If you are not afraid to dig your way through and like to hunt for hidden treasures... 

For indpendent art spaces and young galleries you have to go to the area around the Boekhorststraat. For more details go here.

There are many Indonesian restaurants in The Hague, but this is one of my favorites. Only 3 tables. Mainly take away food. Also very kind staff.