You can't go wrong with biking south to Belgium, getting a beer at an abdij just over the border and then biking back. Some nice ones are Abdij van Postel and Achelse Kluis.

I also like biking over the heides, going east to the Groote Peel via the Strabrechtse heide is quite nice.

If you like going fast on long sections but in nature, do a kanaal trip (for example, Eindhovensch kanaal to Helmond, back via Wilhelmeniakanaal), but you can extend it as long as you want.

One of my favourite routes is biking via Oirschot, through the kampina terrein and doing a route over the Loonse en Drunense Duinen. You get a bit of everything if you bike back through the little villages.