Set in a huge, beautiful park, Konopiště Castle dates from the 14th century and is best known as the hunting lodge of the ill-fated Archduke Franz Ferdinand, whose assassination sparked World War I. He no doubt had a whale of a time hunting in the grounds before he met his untimely end, and now visitors can wander the forests, gaze at the lake, and even watch plays in summer, as well as musing on the Archduke's global significance. In a suitably historic touch, there's also bear who lives in the castle moat; he's a bit shy so you might not see him.
The castle itself is also worth a look, with a carefully preserved interior including many original furnishings from Ferdinand's time. The rooms reflect his incredible opulence as well as his fondness for hunting—there are animal trophies and weapons everywhere. For a properly immersive experience, you can even stay inside the castle walls at a little pension.
Getting to the castle usually involves a ⅓-mi walk through the woods. It can only be seen on a guided tour; book in advance for an English-speaking guide. If one isn't available, ask for an English text to accompany the tour.