One of my favorite spots to walk around is park Belvedere and the neighboring van Stolkpark (separated by a road, which can be closed due to toads crossing it during the spring). It is located between the centre of The Hague and Scheveningen near Madurodam. However, when you walk around it feels more like you are in the middle of the dunes, because of the rolling landscape and the trees. In the van Stolkpark, there is a nice natural-looking pond with a path surrounding it.
This area is also interesting for a different reason, as it was a major part of the Atlantikwall, which was created as a defense against the allied forces during the Second World War and the German occupation. Villa Sandhaghe is located on the edge of the park and was a command post for the German navy. Underneath park Belvedere there was (and still is) a system of bunkers and tunnels. If you walk around the park you will be able to find some entrances to the system (unfortunately not accessible), so it is a nice park with a story to uncover.