Leicester's main municipal museum sits at the southern end of New Walk, a rare pedestrian promenade that runs unbroken through the city. The building is free and covers a lot of ground: an Egyptian gallery with genuine mummies, natural history displays, dinosaur fossils, and several floors of European painting and decorative arts.
The art collection is stronger than you'd expect from a city this size. The German Expressionist holdings are particularly notable — Leicester was one of the first museums in Britain to collect this work seriously, beginning in the 1940s. There's also a good collection of 19th- and 20th-century British painting. Allow two hours for a proper visit; the Egyptian gallery alone keeps children occupied for an hour.