Make sure you get a wooden moai statue or two as a souvenirs for your shelf to remind you of your Rapa Nui adventures. From now and then you'll bump into souvenir sellers, but there are three main places where you can buy souvenirs.
The marketplace is the most accesible shopping site as it marks the center of Hanga Roa. It's located at the intersection where the road from the beach Pea connects with main street Atamu Tekena. Local handicrafts and souvenirs of all different shapes and sizes can be found here; moai statues, moai kava-kava (a skeletal figure), lizards, necklaces and much more. In the morning, fresh, locally grown fruits and vegetables as well as locally caught fish is sold here.
The handicrafts market is located just to the left of the church. This market is dedicated to handicrafts only. Many pieces of art are more pricy here than in the marketplace, but also bigger and more meticulously carved.
Surprisingly enough, the prison also offers some nice shopping for souvenirs. To make time pass, the prisoners make handicrafts, and visitors are welcome to have a look. Prices of the souvenirs used to be much lower here, but since more tourists have discovered this place, the prices are pretty much the same as at the rest of Rapa Nui. The prison is located behind the police station in the area called Mataveri, between the airport and the foot of the volcano Rano Kau.
Except for the three main places with the biggest supply, you'll probably bump into souvenir sellers all over Rapa Nui. There are also many small shops selling souvenirs along the streets of Hanga Roa.