Hi there Bogdan,
The Azores are a great deal, especially if you are flying SATA from Boston! Assuming these are the flights you are looking at, you’re probably going to fly into Ponta Delgada. Sao Miguel is a fantastic island, but the diving isn’t the best if you are just doing day trips from PD. However, most of the dive operations are easily accessible within the city. They are located in the east port (just to the other side of the public swimming pool) and most of them have great reputations.
With that said, you should really consider taking another hopper flight to a different island if the mako and blue shark are your goals. Unfortunately the islands can be quite far apart and links between the main islands can be infrequent. Santa Maria tends to be the most popular with divers. This island features 10 dive sites with some good pelagic encounters. In the summer, whale sharks arrive. At other times, you might see a sun fish. The dive site in Ambrosio sometimes plays host to dozens of mobulas.
A second choice for you might be Sao Jorge. This island receives a lot of strong current that draws in many pelagic species.
Finally, if you can find a liveaboard or dive shop to take you to one of the seamounts in the Azores, you are sure to see many of the great pelagics in the area. Princess Alice off of Pico Island is called one of the best sites in the Atlantic. Here you will also find hammerheads, blue sharks, mobulas and dolphins. Condor Bank is also home to several shark species including the mako shark. And the Formigas Islets 20 miles from Santa Maria are victim to strong currents but feature sightings of Galapagos sharks and giant oceanic manta rays.
July, August and September are going to produce the best blue shark sightings and the most comfortable diving.
There is so much choice in the Azores for pelagic lovers. If you have any other questions about the weather or the best time of year for these species, you can take a look at our Azores entry at
https://diviac.travel/d/azores. Happy diving!