Beautiful view and fountain.
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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.
Small ruin close to the observatory. Nice view.
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)
The Bohnenviertel is the only preserved part of Stuttgart's old town, having miraculously survived to the present day largely intact. Built mainly in the 14th century, it used to house the poorer part of the population, who fed mainly on beans which were grown all around the quarter in gardens and even hanging from the houses' walls, hence the name meaning "bean quarter". Today, the Bohnenviertel is thriving on artisanry and small, old-style retail, as well as gastronomy and red light district.