Great place in Imerovigli, ideal for a honeymoon, very calm and beautiful place. Don't hesitate to book, Anna is very helpful and very nice !
If you like Greek cuisine, you can go to Anogi restaurant, and Avocado, they are great :)
As for La Maison, amazing view but expensive for what you have in your plate.
Don't hesitate to book the sunset cruise tour recommended by Anna, it is not cheap but worth every penny. We had an amazing time!