Songo Mnara sits a few kilometres south of Kilwa Kisiwani and is reached on the same boat trip — most operators combine the two. The island is smaller and lonelier than Kilwa, with no current population, and the ruins survive in remarkable condition: five coral-stone mosques, the courtyard houses of merchant families, and the small Sultan's palace at the centre.
Half a day is enough to see the site properly. Take water; there is no shade in the heat of the day, and the local guide will only really know the layout if you press for detail. The fact that you can have a perfect medieval Swahili town effectively to yourself is the point.