On the island of Nusa Penida, you can hire a moped and make the journey to Kelingking, which is about 30 minutes from the harbor. A restaurant is perched on the mountain with some pretty extreme views.
The safety at Kelingking is reliant on the bamboo railing. At many points along the cliff edge, there is no rail whatsoever and the grass just leads you off the edge, down hundreds of feet onto the rocks. The lack of safety should give you no false sense of security, be very careful as you walk along the edge enjoying the view.