I just wanted to pop back in here for @Telemark, as I did end up jaunting over to the Azores at the end of June and I said I would report back.
The first thing I learned was that the name is pronounced ah-SZORES, not AY-zores. So now you can fit in like a local 
My wife and I enjoyed our time there quite a bit: the landscape is beautiful, it’s easy to get around (with a car), speaking English was not a problem, and most everyone was friendly. The flights to/from Boston were quick and easy - we had some minor delays, but nothing serious (which we feel very lucky about, given the crises at airports these days). We stayed entirely on the main island, Sao Miguel.
The most difficult part for us was the weather. Our plan for this trip was largely hiking mountains and finding beautiful vistas (of which there are a lot). We were well aware that it’s humid and variable, but end of June/early July is supposed to be the dryer part of the year. Not for us. Almost every day the clouds rolled in from the north, collected on the mountains in the middle of the island, and kept many of the high vistas enveloped in clouds. There are webcams across the island, so you can look to see how the views are at any time, and we spent a lot of time (too much!) monitoring these cams to see where the best weather was and adjusting our plans accordingly. That was honestly a bit of a drag, and there were a couple of places we didn’t get to go because they were just clouded in the whole time.
In general, the south coast stayed pretty sunny, though, so we spent more time down on that side of the island and we really only got drenched on one hike (our first one!) before we figured out how to maneuver around the clouds.
We loved the Terra Nostra botanical garden, got in a bunch of waterfall hikes, some of which you can jump in for a swim (cold!!), walked some beaches, visited the only remaining tea plantation in Europe, drove to scenic lookouts (Miradouros) all over, and explored small villages around the island.
The food was OK. (My wife has food allergies, so eating while traveling is always a challenge). If you like fish, you’ll be in heaven. If not, less so. Quite inexpensive, though, which was great.
Overall, I enjoyed it and am glad we went. Not my top trip; I’d give it maybe a 7/10 due to the weather issues. But I’d still recommend it as long as you go in with open eyes.
