If you do visit the Citadel, don't waste your time and money at the Divan Café: The desserts were stale, the coffee was cold, and the service was extremely slow—given that we were the only two people in there and the wait staff consisted of four people.
Inside and outside the Citadel are various specialty and gift shops. Most shopkeepers are great, but if you encounter pressure, just walk over to the next one. Most of the stuff they are selling, while decent, is not terribly original, and you might have a more fun and relaxing atmosphere, and pay lower prices to boot if you don't yield to pressure. If the shopkeeper does not ask you if you'd like some tea or water, it's a sure sign they just want to grab your money and be done with it.
For a variety of olive and olive oil related products, visit zeytinhane, right across from the gates of the Citadel.
Oh, and don't give any money or goodies to the swarms of kids who go surround you and shout facts in various languages. It will only encourage more and mark you as a target for the occasional pick-pocket.