This is one of the first questions that occurs to many folks who read the stories. There is no town that is named Rocky Beach California. However, Robert Arthur apparently based it on a town that he knew of, because there are very specific references to distances from actual cities. In fact, in "The Mystery of the Whispering Mummy," Robert Arthur says that Rocky Beach is 15 miles from downtown Los Angeles (p. 123 of the US hardback version). Also, Rocky Beach is described as being 10-12 miles from the hills outside Hollywood (p. 14 of the US hardback version). With such detail, it seems that Arthur was basing Rocky Beach on an actual town. By its name, Robert Arthur obviously intended for the town to be on the ocean; so the task is to find the right town.
I'm not a California resident; so I may not have the proper perspective to make the best guess of which town was intended. However, in playing detective a little, it seems like Topanga Beach may fit the bill. First, Topanga Beach is described as a "rocky beach" on several websites (as opposed to a sandy beach), the name "Topanga" is Shoshonean and means "over" or "above" and (apparently) has the connotation of mountains or large rocks. Finally, the shortest driving distance from Topanga Beach to Hollywood is 17 miles, and the shortest driving distance from Topanga Beach to Los Angeles is 21 miles. Not exactly the numbers that Robert Arthur used in "Whispering Mummy," but not too far off either.
Another interesting possibility is Ocean Park, which (not coincidentally) is 15 miles from Los Angeles and 12 miles from Hollywood. It's also possible that he used Santa Monica, but since that town is relatively well known, it does not seem as logical a choice.
I've never been to either place. If someone else has an idea of which one (or a different town) is more likely to have been the intended "Rocky Beach," let me know. Below is a map that shows both towns in relation to Los Angeles and Hollywood.