I would take the first one or two nights in Sultanahmet and the rest at the Bosphorous, as others have recommended. Most tourists will want to see the old city -- Blue Mosque, Hagia Sophia, Basillica Cistern, Grand Bazaar, Topkapi Palace, etc. These locations are within walking distance of the FS Sultanahmet; plus the ambiance is nice in that part of town and the hotel and service are beautiful. (One small benefit is that the Sultanahmet is closer to the airport, by a significant margin at certain times of day depending on traffic.)

Now that I am a semi-regular to Istanbul, however, I stay on other side of the city, e.g., the FS Bosphorous, especially in summer. I have said on this forum many times that the setting at the pool along the Bosphorous during the summer at either the Kempinski Cirigan Palace or Four Seasons (which are next door to each other) is among the most picturesque places I have ever been. Plus that area is close to many sites worth visiting -- the greater Taksim neighborhood, Macka, Ortakoy, and walking along the Bosphorous in general.

I agree with schriste, the rooms are the Park Hyatt are nicer than the FS Sultanahmet (and also nicer than the FS Bosphorous or Cirigan Palace, for that matter). Plus I find the FS Bosphorous rather ugly from the outside. Still, it's a special location that is certainly worth a stay.