We chose a liveaboard over just day trips as you can reach the most popular dive site of 'Princess Alice', its a deep ocean pinnacle that sits at 35m and attracts huge schools of Mobula, Jacks, Tuna and Barracuda, I have never seen so many fish at once in all my life! We did mostly line diving here, we saw hundreds of Mobula at once and I was lucky enough to see a whale shark here too! Then for the Blue Shark dives its line diving also and we got to dive the whole day with them. We would drop down on the line at around 8m and just sit there and watch as the Blues came up and touched us and swam between us and around us, it was amazing! Then when we got low on air we would go back to the boat and change our tanks to come straight back down when we wanted to. The shore dives were ok, but nowhere near as exciting as the deep stuff, it also got a lot colder closer to the shore, a lot of the other divers with us did love the topography of the closer sites though. I feel the cold a lot and was wearing an 8mm suit with hood and gloves (you have to wear gloves around the Blues) but next time I would bring a dry-suit! We also saw dolphins, false killer whales, turtles and a baby sperm whale from the boat which was super cool!
We climbed Pico Mountain, a dormant volcano, at the end of our trip; (don't forget your no-fly times as it sits as 2300m high). I definitely recommend going with a guide for the hike and be prepared for a long day, we took around nine hours in total and we wernt the slowest, but the view from the crater (on a good weather day) is worth it; we could see the other islands of Faial & Sao Jorge.
We hired a car to explore, as you can make it around the island in around two hours, we did it in six as we stopped at every single viewpoint and meals too. There are so many beautiful stops along the way where you can enjoy the view of surrounding islands, the Unesco heritage vineyards and the black lava that covers most of Pico.
We took another day to explore Faial, which was only a short ferry ride. Horta is the town here and is the midway point for boats when crossing the Atlantic, it was lovely to see all the different boats and to explore the streets and old buildings.
I would definitely dive the Azores again, although next time with a dry suit!