The Schlossgarten is the old ducal garden, laid out in the English landscape style with lawns, ponds, mature trees, and curved paths instead of stiff baroque geometry. It is quiet enough to feel like a break from the city, but close enough to the centre that you can use it as part of an ordinary sightseeing loop.
Come here after the castle rather than treating it as a separate expedition. In spring and early summer the plantings make the garden especially pleasant.