Although
>>1065550 has a point, there are some things you can do.
THe best is to take the 3-4 hour drive to the German Eifel. If you are looking for multiday hikes, the 'Wildnis Trail' and the 'Eifelsteig' are pretty good. Otherwise, you can find a place to stay for pretty cheap and just do day hikes.
The nearest thing that can pass for a forest in the Netherlands is probably starting at Ziest and then going eastwards. There will be some pretty nice areas, but they'll be small and you'll meet plenty of people.
If you're looking for a multiday trail in the Netherlands, go do the 'Pieterpad' or bits of it.
Also, there is the Biesbosch, but it's mostly insects and swamp. Nice to rent a small boat though.