Four km up the dirt road leading north from the museum is Motu Tautara, the first of two long lava islands pointing straight out from the coast. As you head down to the viewpoint over the islands, watch carefully on the left for the tiny entrance to Ana Kakenga, the Cave of the Two Windows. It's not far from the coastal road, near a curve in the track, and is easily missed. This remarkable lava tube gets much larger inside, with two openings in the cliffs directly above the sea.
A km north again, near where the rough coastal road turns sharply inland, is unrestored Ahu Tepeu and its fallen moai. The site is between the stone marker and the coastal cliffs, beyond the foundations of some canoe-shaped and round houses. Go around to the back of the ruined ahu to appreciate the megalithic stonework. In ancient times this area belonged to the powerful Miru clan.
Ana Te Pahu, a km southeast of Ahu Tepeu on the road inland, is one of the most spectacular lava tubes on the island. There's a stone marker but you'll know the cave from the banana trees and taro growing up through openings in the rock. You could drive a large truck a long distance through this cave (have a flashlight with you).
Inland again via the dirt track is Ahu Akivi (Siete Moai), with seven statues restored in 1960 by Dr. Mulloy. The seven much-photographed moai once overlooked a village but they now stare silently out to sea. Unfortunately, agricultural development in this area has obliterated many archaeological remains. If you're walking, the dirt track which begins opposite the nearby farm entrance, a bit back toward the coast, runs directly south to Hanga Roa. This 13-km circle hike can be done in a day if you're fit and have food and water with you.