Built by the King of Wolega in the 1870s, the Kumsa Moroda Palace has only recently been opened to the public after long years of neglect. It sits 1km north of the museum and served as residence to the prominent Worra Bekere family until they were hauled off to Addis Ababa during the Derg. The compound consists of around 10 buildings, and admission includes a guide who can explain what each building was used for – expect enthusiasm but not perfect English.
Outside are a number of places to get a traditional Ethiopian coffee in a park-like setting. Note that opening hours of the palace are a little flexible and on Sunday morning everyone is likely to be at church.