Take the tram to Eminonu. Visit the large New Mosque near the tram stop and then walk a short distance to see the beautifully decorated Rustem Pasa Mosque.
Walk the small side streets to the Spice Bazaar. This L-Shaped market is not as large as the Grand Bazaar and much more manageable. I loved buying spices and my new favorite olive oil soap. Having lunch at the second floor restaurant, Pandeli, is a must. At the water side entrance to the Bazaar take the stairs to left. (right side as you exit). The restaurant is beautifully decorated with blue tiles and has great food. Try to get a window table to see the water.
After lunch, take a cab to the Kariye Museum (Chora Church). Also in the 1000 Places to See Before you Die book, this is a little-known mosque-turned museum that has dazzling 14th century mosaics and frescoes depicting biblical scenes as well as some of the most important and extensive Byzantine paintings in the world. There are some lovely cafes at the exit where you can have a cup of tea and a baklava to end the day. The address is Kariye Camii Sokak, Edimekapi 90, phone 0212 631 9241. Closed on Wednesdays, it is out near the western wall.
Try Hamdi restaurant for authentic Turkish cuisine; I did not have the chance, but it was recommended and is not too far from the Spice Bazaar.