The Mausoleum of Bin Ali is a quiet religious site just outside Mirbat, built around the tomb of a 14th-century local Islamic scholar. The whitewashed mosque and the cemetery around it make a good counterpoint to the town's forts and merchant houses, especially if you are interested in Dhofar's older coastal culture.
This is still a place of worship, not a museum. Dress modestly, remove your shoes before entering the mosque area, and give people space if prayers or family visits are taking place.