The Ashmolean on Beaumont Street is the oldest public museum in Britain, founded in 1683 when Elias Ashmole donated his collection to the University of Oxford. The current building is a grand neoclassical structure from the 1840s, and the interior was comprehensively redesigned in 2009 to create a museum of real quality. Admission is free.
The collections span antiquity to the present day: Egyptian mummies and Greek bronzes, Raphael drawings and Pre-Raphaelite paintings, Indian sculptures and Japanese lacquerwork. The archaeological holdings are particularly strong — there are important finds from Egypt, Nubia, and the Near East, as well as exceptional objects from ancient Greece and Rome. The department of Western art includes paintings by Titian, Uccello, and Holbein, and a room dedicated to the Pre-Raphaelites. You could spend three or four hours here without exhausting what's on display.