Ras Mkumbuu is the headland at the end of the thin strip of land jutting into the sea northwest of Chake Chake. It's also the name given to the ruins of an ancient settlement, once called Qanbalu, dating from the 8th century, which by the early 10th century had become one of the major cities along the East African coast. The main ruins, consisting of a large mosque, some tombs and houses, date from around the 14th century, and several walls are still standing.
Ras Mkumbuu is about 10km from Chake Chake. Dalla-dallas run as far Wesha but after that transport is erratic, and you may have to walk. Other options are taxi or rented bike, or a boat from Wesha.