There is a great restaurant in Sant Joan de Labritja called Cafe Giri. It's up in the North Eastern part of the island near Portinatx. The chef there used to run El Bulii in Barcelona. The food and wine are both amazing.
Probs the best restaurant in Ibiza right now! Amazing modern surprising cuisine.
The North is stunning, defo worth visiting. Quick list of some of the faves: Benirras; stunning beach with a few great restaurants, Elements is the best one imo. Rent a paddle boat with a slide and get out of the bay for a swim and snorkeling. Portinax is very pretty with some good restaurants. Cala San Vicente is sweet too, the restaurant on the right side of the bay with Dutch owners has great food.
If you're going with your missus, go and visit Hacienda na Xamena hotel, it's super scenic and has a great spa over the cliffs and a very good restaurant. You can pop over for a lunch and have a swim in their gorgeous pool. Another stunning place up north is Atzaro. Very romantic, lovely food and a lot of fun stuff like fashion shows happening in the evenings. There's a dj and a great cocktail bar that's open pretty late. Aura is also a good option for a civilised "night out", they have a big garden bar and a little dance floor indoors.