Tarantula is a 1955 science fiction film directed by Jack Arnold, and starring Leo G. Carroll, John Agar, and Mara Corday. Among other things, the film is notable for the appearance of a 25-year-old Clint Eastwood in an uncredited role as a jet pilot at the end of the film.
The scenes with the spider at the rock formation was shot at the Dead Man's Point cliffs. On the other side is where the spider first showed up in full size when it pushed rocks towards Dr. Matt Hastings and Stephanie Clayton when they visited the site.
http://en.wikipedia.org/wiki/Tarantula_(film)