There are so many castles in Germany! We've been to a few and tend to save them for when we have guests to show around. Burg Hohenzollern is a castle that is close by to Stuttgart. An easy half day trip. You buy your ticket in the shop by the parking lot and can either hike up to the castle or take the lazy man way (which we like) and ride a bus up the mountain. Don't bother paying for the tour inside. We did and did not think it was worth it. It was nice to just walk around the outside and enjoy the breathtaking views!
Linderhof and Neuschwanstein
Linderhof is a great castle to do with visitors. The tour inside is worth it. And the grounds are so pretty. It was Kind Ludwig's summer castle.
Neuschwanstein is the castle that Disney one is modeled after. We did not do the tour inside as we had heard it was not worth it and the lines were super long. But we did take the bus up to the castle to check out the courtyards. You can hike up there too! Once up there, follow the signs to the bridge. The bridge is a great way to take photos of the castle.