I'm an absolute Istanbul junkie, so much so that I try to go there every year. I'd say that a week is the bare minimum to do justice to that great city. If you want there are some great islands just off Istanbul that are worth an excursion (Princes' islands I mean).
If you want here's an idea of how to spend the time.
Day 1) The basics. Blue Mosque, Suleymaniye, Ayasofia.
Day 2) Maybe more time in the Spices bazaar and surrounding alleys than the Gran Bazaar. Definitely a stop at Kurukahveci Mehmet Efendi to buy some of the goods. Topkapi since time won't be enough on Day 1 to do it justice.
Day 3) Galata, Fener & Balat. Get yourself to see St Mary of the Mongols. Walk the crumbling roads in those neighbourhood. Get a vapur up the Horn and go see the view from Pier Eloti. End the day in Istiklal, or perhaps start it too; get a good Turkish at Mandabatmaz.
Day 4) Get from Besiktas to Beyoglu to Ortaköy. Spend some time there, then jump on the other side to Kuzguncuk. Just sit down and watch the ships cruise in the Bosphorus.
Day 5) Spend a little time in the southern part of Sultanahmet; Little Hagia Sophia is a jewel. Then get a vapur from Eminönü and go to Kadiköy and down to Moda. As it's so cheap I'd even recommend doing some vapur hopping, it's intoxicating.
Day 6) Princes' islands.
Day 7) to cover anything else.
My 2p's worth.