It's a bit confusing because there's the Asian side and the European side of the *Bosphorus*, then there's the sides of the Golden Horn, the old side and the new side (roughly north and south.) The old side of the Golden Horn is where the Sultanahmet is, with the Blue Mosque, Topkapi, etc.
Here's a little map that kind of lays it out:
http://www.turkeytravelplanner.com/go/Istanbul/index.html (great site, by the way.)
