Actually, that is along the Cliffwalk in Newport, Rhode Island, and yes, you can visit the site. It's located not far from Seaview Terrace, the original Collinwood. You go down some stone stairs and as long as it's not high tide, it's pretty safe.
I believe it is most likely the Cliff Walk in Newport RI, which is near the Carey Mansion/Seagate Terrace. However, the entire shoreline of this seaside city looks about the same, all rocky beaches. A road runs along the shoreline, called the Ten Mile Drive, there are many places where you can stop and look out over the ocean, it's very picturesque. The ocean could have been photographed just about anywhere along this road.
I have to agree that it is most likely filmed along the cliff walk in Newport. Maine has always seemed like a stretch since nothing else was filmed there.
The area near Seaview Terrace has high enough waves to attract surfers who call that section Ruggles (the street you take to get there.) I don't know when the DS film crew showed up in Newport but the remnants of hurricane Alma would have passed by Newport on June 14th in 1966 and that would have created even higher waves. Last one of the promotional photos I have seen of Alexandra Moltke (marked #DS7017) was taken in that section of the cliff walk with Ochre Point visible in the background. All the pieces of the puzzle seem to point that way.
The exteriors at Newport, including the ocean, were filmed in the spring of 1966, before the first episode was taped, so before the storm of June 14.
The waves intro was filmed in Newport.
There's a YouTube video showing a short minidocumentary made in 1985 where Jonathan Frid serves as a tour guide for the grounds of the estate in Newport used to represent Collinwood. Before visiting the outside of the Black Pearl, used to represent the Blue Whale, Frid shows us the cliff walk area used to represent Widow's Hill, and points toward "the breakers, the world famous breakers, is right over beyond the white gabled house that you see at the point..."
Thank you, Prisonerofthenight, for sharing that link. After 40-some years, I am going to visit these sites this summer with my family. It feels a bit surreal and at the same time, like my life will come full circle. I can't wait.