Ludwigsburg Palace is one of the great Baroque residences of southwest Germany, large enough to feel like a courtly town rather than a single building. State rooms, ceremonial staircases, theatres, museums, and formal gardens show the ambition of the Württemberg dukes just north of Stuttgart.
It is outside Stuttgart proper, but close enough to be one of the city’s best day trips. Give it a half-day if you care about architecture or gardens, and check which guided tours and seasonal garden displays are running before you go.