Thanks so much @peter_v and @greeno! I'll definitely go to the Mauritshuis, I was a bit disappointed when I thought it was closed. I've just seen that it's 14euro entrance, eek - I forget how spoilt we are in the UK with free museums and galleries!
I'll have cycled to the Hague from Berlin so I'm all up for a day of just wandering about - and I do love a chilly windswept beach (I'm not joking). Sounds like the Hague is going to be right up my street!
Another question - any particular recommendations for a veggie (or veggie friendly) restaurant? Thanks! :)