The region of Tissa and Kataragama has great religious significance, but unless you are looking for n affordable hotel by the lake at Tissa as a base for Yala there are not too many specialist family-orientated activities in this region.
However, about an hour’s drive inland, en route to the hill country, lies the game park of Uda Walawe which does not have the range of wildlife enjoyed by Yala, but which is comparatively quiet and will satisfy any craving for watching Sri Lanka elephants in the wild. Of particular interest here is the Uda Walawe Elephant Transit Home which exists for the primary objective of rehabilitating orphaned elephant calves before releasing them. A good, environmentally responsible activity for families.