One day I took a new, compact metered taxi and toured some of Jaffna's outlying islands. Karaitivu, Kayts and Punkudutivu are all connected by causeway, ferry and bridge, and can be reached by a car from Jaffna city. I drove in a loop around all three.
There is little in the way of conventional sights, other than the poignant sight of war-damaged houses in fields or half hidden by tropical foliage. The main attraction is the otherworldly feeling of remoteness and the beauty of the blue-green sea.
Other islands further afield, accessible only by boat, would also be worth visiting.