I'm sorry to have to break this to you, but...respectfully, 10 to 12 days for all that is simply not realistic (in fact, it may not even be physically possible, even if all you do is move from one place to the next and spend zero time actually being anyplace).
I spent 3 weeks in the Azores last year. We had a full week on São Miguel alone and we had wished we had budgeted 10 days for that -- one island (we did 6 of the 9 islands in 3 weeks and we were moving fast). The Azores really deserve more time (and requires it, too, if you're planning to "island hop").
Likewise, mainland Portugal is worth more than 3 or 4 days (which is about how much time you'll have if coming from the US west coast and stopping in the Azores).
With just 10 to 12 days, pick either mainland Portugal (Lisbon + Fatima + Porto - there's your 10-12 days), or if you want to skip the mainland and just do only the Azores, do São Miguel + one or MAYBE two other islands (São Miguel + Faial + PIco, or just São Miguel + Terceira). The connections between islands are not as quick/frequent/convenient as some would hope/expect.
Or increase the number of days you have (by a lot!). Ten days for a trip to Europe from the US west coast does not give you a lot of time at your destination, whatever that may be. Sorry, I know this is not what you will want to hear, but...I think you simply have too little usable time for all those places, and spreading your usable time across many places in that short a time would not result in a trip I would enjoy.