The feet and lower torso of the Monster suit were were recycled from the "Metaluna Mutant" in This Island Earth (1955), with the claws being recycled from the creatures in The Mole People (1956).
Piedras Blancas (Spanish for "White Rocks") actually exists. It's a promontory on the central California coast and it does have a lighthouse that was used in this film, but only for exterior shots.
The exterior and interior lighthouse location used in the film is the Point Conception Lighthouse in California. The same location was used in Brave New World (1980).
In 1965 the monster costume for this film was used in Flipper's Monster (1965), in which film crew is shooting a "monster movie" in Florida. That episode was directed by Ricou Browning, the show's creator, who coincidentally was best known for playing the "Gill-Man" in Creature from the Black Lagoon (1954), which was the inspiration for "Monster of Piedras Blancas".