I have never sailed on Princess, but we sailed on the Atlantica in April and absolutely loved it. She was a gorgeous ship with lots of fantastic quiet spaces.
The muster decks/promenade NEVER had traffic. There is nothing located there so they are always empty. However, there is a lot of shade and a few benches.
The indoor Garden Terrace on forward part of Deck 3(?) was always beautiful and quiet. I NEVER saw anyone sitting there no matter what part of day I passed through. That might have been because you could feel quite a bit of motion in this part of the ship. That doesn't bother me, but it might with someone else.
The Chapel in the forward part of Deck 4 is fantastic and quiet. Beautiful stained glass windows and statues - very peaceful - it is well worth a visit (even if you are not a religious type.)
By the way, Costa does not allow you to bring alcohol aboard - not even wine. However, there are several wine packages available.