From the old bridge, instead of turning right to Shri Omkar Mandhata, head left and walk up the 287 steps to the 11th-century Gaudi Somnath Temple, from where you can descend the hill to the northern tip of the island, where sadhus bathe in the confluence of the holy Narmada and Keveri Rivers. You can climb the narrow, inner staircase of the temple or just sit and watch the langur monkeys play. Nearby is a 30m-tall Shiva statue.
