Oh, I love the Four Seasons Istanbul as well, but don't know your budget.
This is where I stayed on my last visit.
Uyan Hotel Istanbul It is located one block away from the Four Seasons. We had a lovely, very large air conditioned room with breakfast for a significant amount less (read: fraction of the price) than you will pay for the Four Seasons.
Regardless of where you stay, please, please have your hotel make reservations for dinner at Hamdi. The food is wonderful, but the view and ambiance are something you will remember forever!