Small ruin close to the observatory. Nice view.
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Beautiful view and fountain.
State Gallery
There are two exhibitions in different buildings. "Alte Staatsgalerie" ("Old": Art from 1500 to 1900) and "Neue Staatgalerie" ("New": Modern art). You can walk inside from one exhibition to the other. The permanent exhibits are free on Wednesdays and Saturdays.
A fascinating astronomical journey, projected by optical hightech equipment: Carl Zeiss Planetarium. Almost all the shows conducted here are in German. You may have to check with the office for English show timings.
Watch and listen to the ballet company of the state theater Stuttgart. It is one of the world's best ensembles founded by legacy of John Cranko. Definitely a top place to go to in the evening. You'll need to reserve tickets in advance.
King William's Palace
(1834-1840)