Easter Island
I know you mentioned wanting to live there for a month. I honestly, wouldn't recommend it. I visited over Christmas with my partner. While not specifically antagonistic, it wasn't the most open place we visited (SCL & EZE were the others, heck IST even is).
Plus, to be honest, it's a great place to visit... once. It's very expensive since almost everything is flown in.
Take a look at Santiago, you could help with some of the quake recovery if you liked and the city is very nice.