There was an anime I saw one time before I actually got into anime, and I'd like to figure out what it was. There are only a few things I remember... There was a big mysterious statue of a hand (on a mountain?) that you could see in the distance. I think I remember one character saying he didn't know what the statue was for. The only other thing I remember is a lonely girl walking by the water in a dark dreary town (smoking a cigarette even though she seemed young) and a weird little machine jumped out of the water. I don't think the machine talked, but the girl interacted with it. That's all I remember. Does anyone know what it was?
At least the second part of your description definitely matches FLCL (Furi Kuri):
Plot Synopsis (from wikipedia):
The lonely girl you were talking about, is the (maybe ex-) girlfriend of naota's big brother (Mamimi Samejima). She meets a small metal-eating robot when she smokes a cigarette under a bridge. The robot gets larger and larger the more she feeds him.
On the "mountain" in the town there's a humungous smoothing iron, which is supposedly lifted by a giant hand, to smoothe earth in preparation of an invasion (if memory serves right, that is).... Well at the end of the story, the hand gets petrified, which gives us this wonderful final image: