Easter Island is a place that any adventure traveller should spend the time and money to visit. If you are Australian, heck, you can do it on the way to South America, just book a flite that stops there to refuel in either direction (LAN) and pay the bit more to do a layover.
The first thing everyone notices when you land is the incredible size of the airstrip! This is the first mystery of the island. But the answer to why is simple. It is an emergency landing strip for the space shuttle! While I was there, the space shuttle was up, and two astronauts were "in residence" as they always are during a mission. I met them, really superb human beings.
You do not have to worry about accomodations. When you get off the plane there will be a dozen or more families there with pictures of their house, the room they will rent you, the bathrooms and meals they will serve you. Negotiate a price. Once you have agreed, they will slip a flower lei around your neck because you have been claimed and the other families will not approach you anymore. Quite quaint.
You can get around the island hiking, biking, motorcycles or horse back. You will be offered the chance to rent any of the last three by your hosts. I rented a horse the first day. The horse and I did not get along so well, so I rented a moto for the rest of my stay and zipped all over. It isn't that big of an island, but you want to see it all.
You have all seen pictures of the mysterious maori the giant statues with face that look like extraterrestials. They are quite impressive in person. It is worth going to each and every site where they exist, they are in many styles and all the sites are beautiful. The quarries where they cut the staues still exist, and some statues lie unfinished, so you can see how they cut them out of rock. It took me about a day of looking at them, and a bit of reading to end the mystery. What else could the rulers do to keep the people busy? Only so many could fish or farm, so this was like a big social make-work project. The other mystery about how they moved them from the inland quarries to the coastal sites is evidenced by the fact that the island is denuded of trees. They had to cut them all down to use as rollers for the statues.
The other place to be sure you visit is the point where the bird people lived. The caves they lived in are still there. It is outrageously beautiful.
Food is expensive, so be sure to eat the breakfast and dinner your hosts should provide and pack a lunch.
Two beaches exist. The rest of the coast is all rock. One beach is popular and crowded on weekends. The other is more remote, smaller and quite nice.
There are some good histories written about the island that you should read before you go or while you are there. It will help to explain the two distinct cultures (long ears vs. the short eared people) that existed there in less than harmony. It will tell you about the tragedy of the Spanish coming and kidnapping the people to work as slaves in the gold mines in Peru. But in all, it will give you a basis for enjoying a spectacular destination. I loved it.
Safe, not cheap.