The Ulm Museum sits right on the Marktplatz and holds one of the largest art collections in southern Germany, spanning from the late Middle Ages to the present day. The medieval section is particularly strong, with outstanding examples of Upper Swabian wood sculpture and panel painting from the 14th and 15th centuries.
The modern wing houses an impressive collection of 20th-century art, including works by Klee, Kandinsky, Lichtenstein, and members of the Bauhaus movement. The museum also hosts regularly changing temporary exhibitions. Combined with the Kunsthalle Weishaupt next door, you can easily spend a full morning here.