I enjoyed this castle and its smaller hunting lodge. When I was there, the lodge at Falkanhurst was open, although the exterior was being restored. The building was small enough that I could imaging actually living in it. The staircase walls are tiled in amazing blue and white patterns, all handmade and definitely worth looking at. It takes a few minutes to walk over to Falkanhurst from the main castle, but worth the walk (it's flat, through the formal gardens, a forest and then across some agricultural land).
The main castle is only viewable on a tour. If you call ahead you can find out when they offer a tour in your language, or they have audioguides in different languages that you carry with you on the regular German tour. The staircase is pretty impressive, all Baroque and curly and ornate. One wing of the castle is used for exhibitions and performances, so you can schedule your visit around what's showing.
We arranged a weekend in Cologne and hit this one, Aachen and the Cologne cathedral in one weekend.