English language on Sanriku Coast

We will be traveling up the Sanriku Coast from Sendai to Miyako, and hoping to visit Ryusendo Cave, Geibikei Gorge, and the Kitayamazaki Cliffs, among other spots. What should we expect in terms of English language communication? For example, will there be English speaking guides at the Cave and the Gorge? Are important road signs in Japanese and English? Should we expect at least some of the staff at restaurants and shops to speak English?

The Sanriku Coast is pretty much the same as elsewhere off the main tourist routes:

You should generally not expect people to be able to speak English.
You should not expect any English speaking guides.
Important road signs are generally bilingual.
You should not expect staff at restaurants and shops to be able to speak English.

Thank you for this answer. Just to make sure I understand correctly, some of the tourist spots we are interested in, and the hotel we have a reservation at, have extensive websites in English. Is it true that this does not necessarily mean there will be anyone at these locations that speaks English? Even if the websites are translated entirely into English?

Hotel receptionists usually speak enough English for the check-in process (there's not much needed anyway), and to explain how the hotel works. But they might not always be able to answer, for example, if you ask for sightseeing/restaurant recommendation. Yes, even if their website is fully translated in English.

Of the locations you listed, I only went to Sendai and Geibikei. At Geibikei, the boatman definitely did not speak a single word of English (I would have been really surprised if he did!).

Frankly, even in places on the beaten path (Kyoto comes to mind), you should ask for the Japanese menu and translate it yourself. I had a few occurrences where the English menu had significantly less options than the Japanese one.

Would you expect that to be true in Zao Onsen as well?

My general rule/observation is that once you move away from the regular tourist spots English dries up very quickly. That is true in Tokyo and Kyoto, but more pronounced in smaller locations too.
Having an English version of a website doesn't tell you much about the language ability at a particular hotel, especially if it is small. Machine translations can generate those web pages in seconds, but it might not have been done with someone that actually speaks the language.

After extensive travels in Japan - finding a person who speaks reasonable English is more an "exception to the rule" than what is expected when visiting rural Japan.

I've visited the majority of the locations you have mentioned - albeit quite a while ago. It's rare for people to speak reasonable English. I'd compare it to expecting people in rural Australia to speak Chinese. There might be the odd person - but it's rare.

I can also confirm that an English website does not confirm that a location has someone that speaks English on location.

This might seem like doom and gloom - but if you take your time and use simple wording in Google Translate, basic questions can easily be answered at hotels.

Your biggest problem will be at restaurants which write their menu by hand as Google Translate will not be able to translate these. Note that I speak next to no Japanese and found it relatively easy to move and live around Japan if you try and meet half way.

Just learn a basic few words in Japanese and use Google translate with the camera function and you will be fine.

You will be fine. The hotel staff may not speak English but will almost certainly be used to dealing with foreign tourists. Printed copies of reservations are a great help for hotels. As has already been said Google translate is very good these days & will help you out with menus and signs. A friend visited similar areas just pre covid & only knew the Japanese for Hello, Goodbye, Entrance, Exit, Beef, Pork & Fish. She had a fantastic time.
It sounds like a great trip & is an area that I hope to get to soon. Have fun!

On the hand written menus - most restaurants don't have hand written menus. This is more common for restaurants which serve the local population and is often a "mom and pop" location or local izakaya. Many chain restaurants (including Japanese) now even have touch pads (often in English) or large menus that might even be in English.

Having an English-language website has nothing to do with the quality of language ability among the workers you meet at that specific hotel. It just means that the hotel was able to afford a good translator and web designer who work elsewhere. It's not that people who actually greet you there had translated it. That hardly happens.

But having an efficient English website (while many are out of order) implies that the hotel is willing to accommodate guests with language barrier. Either way, all you have to do is to send some kind of an inquiry (such as "Do you have English-speaking staff and English menus?") and see what kind of a response you get. If you feel that the response suits you, then the hotel would most likely suit you to a certain extent.