The German word for castle is either a "Schloss" (more like a palace) or a "Burg" (like your traditional stone castle and moat).
The most famous castle near Munich is Neuschwanstein. This is the fairy tale castle built by King Ludwig of Bavaria, aka the Disney castle. It is located about an hour south of Munich near a little town called Füssen.
Other castles in Munich are...
- Nymphenburger Schloss
- Schloss Blutenburg
- Schloss Kaltenberg