Dating back to 1843, this massive museum has grown and modernized over the years, especially with the addition of the Neue Staatsgalerie (New State Gallery) in 1984 and a modern hall specially built in 2002. Spanning some 96,875 square feet of exhibition space, the collection focuses on early Swabian panel painting and 19th-century Swabian Neoclassicism, but also includes modern pieces like Oskar Schlemmer’s Figurines for the Triadic Ballet, Matisse’s famous Back Series, and a Joseph Beuys room that was installed by the artist himself. Other highlights range from Dalí’s Raised Instant and George Grosz’s The Funeral to Miró’s Bird with a Calm Look. Opt for a guided tour to ensure you see everything, then visit the museum shop and the Fresko café-restaurant. Note that, on Wednesdays, you can visit the permanent collection for free.