I draw my recommendation for a day walking on Easter Island on a map. The total distance is about 20km.
You start the route with Ahu Riata, which is located directly at the small harbor Hanga Piko. Then follow the road and walk to the cave Ana Kai Tangeta. After visiting the cave, the Te Ara O Te Ao trail starts a few hundred meters later and leads up the Rano Kau volcano as a hiking path, away from any cars. Once at the top, you arrive directly at a lookout point where you can look down into the volcano crater. There is also a stone with a well-visible birdman petroglyph. Then you walk along the volcano crater until you come to Orongo. After visiting Orongo, first head back to birdman Petroglyph and then continue walking along the volcano crater until you arrive on the other side of Rano Kau. On the way there are great views over the Easter Island and at the end of the path you receive a great view of the small island, from which earlier the first egg had to be fetched as part of the birdman cult. Finally, it’s time to go back to Hanga Roa.