Istanbul is a fascinating city. I arrived two days early so I would Traveler's Tip:
Getting over jetlag, step 1: Stay up until as close to a normal bedtime as possible.
have a chance to get over jetlag. It was about 5pm by the time I got to my hotel[*]. I checked in, unpacked, and immediately went out to walk around the city. (I checked with the hotel staff first and they told me that it was safe to wander around at night, even for a woman alone - my first nice surprise of the trip.)

I just wandered around for a couple of hours, trying to get oriented a bit to the layout of the area. I also had fun trying to get some good evening shots with my new camera. That's the great thing about digital cameras - you can snap, snap, snap, trying all sorts of different things, and you don't have to worry about wasting film!