To know where you are the furthest from any building in the Netherlands is very simple.
Buildings in The Netherlands
First of all, you look where all the buildings in the Netherlands are. That is here.
In this picture I represented every building in the Netherlands by a little almost transparent dot. So the black spots is where multiple of those spots overlap. You see some very nice structures in the map. The big white spot in the center of the country is the Veluwe that was mentioned in many other answers. But as you can see, the central part contains some buildings that might kill its top position.
So lets make all dots fully opaque to make sure we don't miss a tiny almost transparent dot. Which gives
Now, we would like to know where we are the furthest from any of those buildings. One option would be to create buffers around each building and increase the size until only one bit of the Netherlands is not covered.
Or to rasterize and get for each raster point the distance to the nearest building. Details of those methods should be asked on gis.
I have used the poor mans version of a buffer: use bigger dots! If we quadruple the dots in size the picture becomes this:
Now we see which places win. Technically it will be the Afsluitdijk and the Houtribdijk (between Enkhuizen and Lelystad). But those are just motorways on a tiny strip of land. That would be a very disappointing remotest place, so let's pretend we didn't see that.
On the islands it is the Eastern tip of Schiermonnikoog that wins. A very quiet place and you can take a decent walk, but the OP excluded the islands.
On the mainland there are four remaining interesting locations:
This is the furthest from buildings that you will get on the Veluwe.
This is the region East of Elspeet. You will get there around 1.5 km away from any building. Not bad, but we had other promising candidates.
Hey, Lauwermeer is something we haven't heard yet in the other answers. It beats the more popular Veluwe. Smack in the middle you would be about 1.8 km away from any building.
After the great post by Belle we shouldn't forget the Verdronken Land Van Saeftinghe. It suffers a bit from the presence of buildings on the Eastern edge, but in the center you will get about 2km away from any buildings.
The Oostvaardersplassen are winning.
Along the Oostvaardersdijk, next to the Oostvaardersplassen you can get as far as 3km away from any buildings. If you want to exclude that for the same reasons as we excluded the Afsluitdijk and the Houtribdijk, you could go the other side of the "plassen" and still be well over 2.5km away from any buildings.
Where to take your walk?
For that little stroll that you had in mind, the Veluwe would be the best option. Neither the Oostvaardersplassen nor Lauwersmeer have walking paths near those remotest parts. They are easier to reach with a kind of boat of your choice.
What about built-up area?
That won't significantly change it. If you look at the maps, you will see that the nearest built-up area is not very far behind the nearest building for each of those places. You will probably get the furthest away from built-up areas by going to the North-Eastern corner of Saeftinghe.
Sources and such
The buildings were extracted from OpenStreetMap, using the most recent Geofabrik builds. In the Netherlands the buildings are in OpenStreetMap are very complete because the official BAG dataset was imported. In other countries the inconsistent quality of the OpenStreetMap data will be a big challenge to repeat this analysis.
The maps that were used as a background are the Bing Maps. All images are my own work.
Some more details, as per request
Download data from Geofabrik. I used the zip with the shape files. Open the shape file with the buildings in your favourite GIS. I used QGIS, but any half-decent GIS will do the job. Add the building layer that you downloaded. I also reprojected to RD-coordinates (EPSG 28992) and converted the layer to a point layer (in QGIS under Vector > Geometry Tools > Polygon centroids). That gives you slightly over 10 million points (10011369 to be exact). It makes the work cleaner and for our purpose the centroid of the building is more than precise enough. Under Style or something you will be able to chose the symbol that represents each point. I picked a black circle corresponding to about 1 pixel with 15% opacity. You have to play a little with the opacity. Too high and you get something like the second map. Too low and Flevoland becomes invisible. But a lower opacity would be better to get some more details in the cities or the Randstad. This is the point where you can be an artist.
For the rest it is merely increasing the opacity to 100% so that every point is obvious, increasing the size of the circle and zooming to the interesting parts. I did it on a 10 year old laptop. More recent hardware would have worked a bit more comfortable.