The whole island, for reasons of landscape, isolation, and history, is of course a very evocative place, but for me the most moving and extraordinary site is the "nursery" at Rano Raraku, so called by the locals because it is where the volcano "gave birth" to the moai. Naturally, it must have been much less poetic than that as a real-live site, and the traces of former activity are still in situ. Each statue was carved by hand from sheet rock, until the contours of its body stood out from the rockface. When a statue's inimitable features were complete and its form stood out proud from the rock, the back was finally (and one assumes very carefully) disengaged and the body somehow lowered to the ground.
It looks as though there was something of a queue to be transported onwards to the waiting ahu and there's no sign these days at Rano Raraku of the tools for moving the statues. However, the new statue was eventually moved to a predestined spot where its ahu was waiting and where it was united with the topknots (carved separately from the red volcanic rock at Rano Kau in the southwestern-most point in Orongo).
Of course, almost everything else is speculation and supposition (which is why a trip to the museum -- see above -- is useful for background and context). It does serve to fire up the imagination though and Lord knows how long it must have taken to carve each statue when the workers didn't have metal tools. They were certainly very skilful though as there's little sign of damaged or broken moai either in situ on the rock or at the bottom. Having seen the statues and realised how much work went into creating each one, you have to imagine that each statue was bespoke and cost a fair deal in whatever the currency or traded goods were, and that the symbolism behind the urge to praise or remember the forefathers was powerful in the extreme; moreover, if the workers were slaves rather than paid craftsmen, seeing the scale of the moai and of Rano Raraku makes you realise how downtrodden they must have felt, putting them on a par with the Egyptian slaves making the pyramids.
It all seems to have been quit all of a sudden, with some moai 300 left still attached, seemingly hanging off the rock or nestled into a crevice. These include "il gigante" which was to have been the biggest by far of the statues (believed to have been 22m) but sadly was never completed or erected. (It's not known where he was to have stood either.)
You drive up towards a car-park from the "main" road and all these little dots are visible ahead from within the grass -- it's only when you get closer than you can make out their forms. It's extremely eerie -- dozens of completed statues seem simply to have been abandoned before transportation to their ahus and, over the years, they've gradually sunk into the soft grass so, approaching from the road, it looks for all the world as though they are growing from the earth itself -- like crocuses, pushing through into the light. It really look like a place of new birth -- unforgettable -- and it sets you thinking that it must have been a big crisis that made the craftsmen and those who had commissioned them give up the statues overnight.
From here, you can also climb up the volcano (mind the ticks and fleas in the grasses!) to get a superb panoramic view of the island, including the coastline and a sunken crater to the volcano in which locals now swim (and apparently fish).