I visited the island in 2003 as a detour in a long trip through South America. Back then there were 2 flights a week from Santiago, the flights continued to Tahiti. We stayed 5 nights, this was plenty of time to see all the Moai and sites.
We know who, when (1250-1500), and where (you can visit the quarry). The mystery is why this was done and how did they transport them from the inland quarry to the shore. It is thought that lots of logs were used to roll them leading to deforestation of the island.
There are lots of ways to tour the island. I chose to rent a motorcycle. These days I would probably rent a car. I also took a taxi a couple of days. I told him when and where to come back for me. This was good and saved money on days when I wasn’t going to go far between places on foot.
There was a lovely beach you could lay on and stare at Moais. There are also a few good scuba diving sites. Including around the famed Moto Nui islet. Known for a local Tangata manu competition.