I dived from Faial some years ago and had a wonderful time, blue sharks between Faial and Pico and Mobula Rays galore (I have a photo with around 20 in and that was tiny part of the group!) at Princess Alice Bank (This was in September).
People seem to think that that Faial/Pico are amongst the best and I wouldn't argue.
My dive with the Blue Sharks will be one of my life highlights, let alone diving one!
Flights to Faial from the UK (and presumably other places) go through Lisbon, which is worth a couple of days on the way/back in itself as a mini city break - We only had 1 day there, but it was well worth the visit.
The Azores is one of the few places I've visited that I'd actually like to live, it's such a lovely part of the world, although the locals tell me the weather can get quite grim in the winter.