Happy to offer some suggestions for you about the Azores. It is a beautiful place and has some amazing countryside and wildlife. The diving is world class and there are plenty of opportunities to dive with Dolphins and Whales in a responsible way. I would definitely bring your photography equipment!
As for staying here, your main island is Sao Miguel - I would start here (especially if you have a family.) We have a family house up for rent that has 4 bedrooms that might work for you, it is being worked on at the moment (ready for a Jan '19 soft launch) so it might be perfect! Check out www.solarbranco.com or email me at email@example.com for more details on that.
On the island there are a number of restaurants to eat in, all are very reasonably priced and family friendly. The island is well set up for tours around and there is plenty for your family to see and do. Flights from Boston are quite frequent and we have met a number of people from the US at the places we have stayed.
Seafood is amazing and fresh, Cais 21 is a great restaurant to eat in, check out this link for more info, http://www.solar-branco.com/guides/
A hire car is a good idea though not essential. The island is easy to drive around and very safe. Hope all that helps and do drop me an email if I can help further.