If you want a good cheap brunch, head up to Cihangir or Taksim for one of the many Kahvalti Salons. Any place with "Van" in the name is sure to be good. A full breakfast (which can feed 2 easily) should run you around 15-16 TL.
For a bit fancier fare, head up to either Ortakoy, Bebek, or Arnavutkoy, all of which are reachable by buss from Taksim or Kabitas. These are all right next to the Bosophorus and are great places to meet Turkish TV stars or to take brunch dates.
Also check out: What are the 10 best restaurants for breakfast in Istanbul?