The Hessisches Landesmuseum is the state museum of Hesse, housed in a confident neo-Baroque building from 1913 at the southern edge of the city centre. The collection runs from prehistoric finds (a famously rich Bronze-Age section), through medieval ecclesiastical art, to Hessian decorative arts and the everyday life of regional villages.
The wallpaper museum tucked into the same building is a quiet pleasure — a serious historical survey of decorative wall coverings from Chinese export silk to 20th-century industrial prints. Allow a couple of hours; combine with the New Gallery a short walk away for a fuller museum day.