Moyse's Hall Museum is one of the oldest (c. 1180) domestic buildings in East Anglia open to the public. It has collections of fine art, including Mary Beale, costumes from Charles Frederick Worth, horology, local and social history including the Red Barn Murder and Witchcraft. Relics of the Red Barn Murder are housed here. They include items that belonged to the murderer, William Corder, including a dagger and sheath, a brace of pistols - as well as his scalp and a book bound in his own skin! His head was kept after his execution, but brought such bad luck to those who possessed it, that it had to be buried.
For further information, please read Haunted Britain by Antony D. Hippisley Coxe.
The Abbey of Bury St. Edmunds (of which the ruins are pictured above) was once among the richest Benedictine monasteries in England. It is now in ruins, but monks haunt them, as you would naturally expect!
For more information, please read Haunted Britain and Ireland by Richard Jones and Haunted Britain by Antony D. Hippisley Coxe.