EvilCastle

Depends on how you do with overnight flights and how much you want to see. There is a ton to see/do in IST.

You could easily see the Haghia Sophia and then the Blue Mosque (or vise versa). They are about a 5-10 min walk between the two. I would go to Hagia Sophia because it closes earlier. I spent about 1.5 hours inside, but its at your leisure so you can spend what you would like. Blue Mosque is a quick visit, but very cool to see.

Then the Grand Bazaar isn't too far from there. Maybe a 15-20 min walk. You can get the experience and maybe find some fun things to buy. There is also the Spice Bazaar...but on such a short trip unless you love Spice's you can skip this.

You could then take the tram over the bridge to the new Istanbul. Or even just get off at the Bridge and walk around. If you like seafood, you can get some fresh food there. Also get get some cheap beer and hang out by the water. (there is another area for even better seafood, but its off the beaten path and will take some time).

Then I'd take the tram up to Taksim square. Cool to see at night time and there is a pedestrian street with shops and restaurants (which leads back to the bridge..so you could always just find it and walk up it after the bridge).

Palaces are nice if you like that sort of thing, but you will have to check if they are open (closed on certain days).

The other option is to spend the afternoon at a Turkish bath and relax after/before the long flight.