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Photo: Björn Appel, CC BY-SA 3.0 via Wikimedia Commons
Although there is no Cologne Cathedral in Stuttgart, there are a few churches worth visiting. Most beautiful is the Johanneskirche, which is surrounded by the lake Feuersee and lighted at night. Other interesting churches are: Mätthauskirche (St. Matthew's Church), Domkirche St. Eberhard (St. Eberhard's Cathedral Church), Hospitalkirche (Hospital Church), Leonhardskirche (St. Leonard's Church), Veitskapelle (St. Vitus Chapel), St. Catherine's Church (English-speaking Anglican Church), St. Maria Kirche (St. Mary's Church).
© OpenStreetMap contributors
Städtisches Lapidarium
Open air museum showcasing ancient sculptures (most of which originate from destructed buildings after WW2), terraces and fountains from Stuttgart's history.
Small gallery with little stores (somewhat similar to Milan's famous gallery but a lot smaller). Right next to it is a building whose exterior is covered with plants.
Culture and Congress Centre
(1956)
Skyscraper from the 1920s. It served as the office for the local newspaper and was the city's tallest building when completed. Not publicly accessible.