The Grand Bazaar is really a city unto itself. The main thoroughfares are where you'll find the most popular shops and restaurants, but just like any city, the coolest spots are tucked away in its less-visited corners.
The lively neighborhood of Zeyrek, just north of the Aqueduct of Valens, was one of our favorite spots in Istanbul. It's difficult to reach with public transportation, and lacks any well-known sights, so very few tourists bother to visit. Not that we mind; it just leaves more Zeyrek for us!