Marcie, definitely try to stay in the Sultanahmet, the old part of the city. It's charming. Aside from the Four Seasons, there are charming guesthouses as well, traditional Ottoman Inns. You can read about them on http://www.turkeytravelplanner.com/ .

Things change quickly, so you might want to get recent reviews on the favorites at tripadvisor.

We stayed the Dersaadet, which was very pleasant. Only downside was a small mosque with a recorded muezzin's call to prayer right outside our window. The rooftop cafe, where we had a very pleasant cold buffet breakfast, had a view of the Blue Mosque, although not the best view probably.