I enjoyed exploring the castle's very large Demense. It has several nice walking paths which take you past some of the more modern residences used after the castle was no long the pinnacle of lordly living.
There are formal gardens/parks, as well as areas left as more of a wilderness. There's a nice walk along a river as well as through several area inhabited by at least two species of deer. I lugged my long Nikon lens along, so got some decent shots.