I recently went to IST on a USAir mileage run (not true run as I stayed for three nights). I was alone and never felt that it was dangerous. Just be smart and don't walk down any deserted alleys at 2 am.
I stayed at the Empress Zoe hotel (www.emzoe.com), which is right next to the Four Seasons and a lot less expensive. The location is perfect, Ann (the owner) and the rest of the staff are extremely nice and helpful, and breakfast is included with the room rate. The hotel has a great deal of charm and leaves no doubt that you are in Turkey. For a six night trip, you might consider staying three nights near the Blue Mosque and three nights north of the Golden Horn.
Please feel free to email me if you have any questions.