Hiya, im not sure if i will be of any help to you, but i have recently came back from working in Ibiza and I found Portinatx is the best place to go where is quiet and relaxing!
Portinatx is at the north end of the island 40 mins approx from airport! It has 3 beaches! (There is a fourth but it is a good hours walk - cala sara) It has only 2 bars and a hand full of shops!
portinantx is based for example in a cove its beautiful and has a superb setting for sunset!
I lived in portinatx and i went for a walk up to a little tower built on the cliff edge up to the left of portinantx and sat up there with my boyfriend and a bottle of wine! really romantic!!!
Not sure if any help but it is a place to be seen!