But where in Turkey? Santorini is a night ferry from Kusadasi area, and more than that from Istanbul. It is not possible to fly direct from Istanbul to Santorini, you would have to change in Athens.
The food is really very similar to Greece, though obviously the culture is different.
Flights from Athens to Istanbul are about 1 hour 15 minutes, but are about $300 round trip. So I suppose you could take an early flight, spend three hours or so, and then head back to Athens and on to Santorini, but I do not think that would be a good use of a day. You would only be able to see one sight, probably just the Blue Mosque and maybe Hagia Sophia.
Turkey is a great destination, and well worth your time to visit, but if you only have a day, I would seriously consider cutting it out. On the other hand, if you can devote two or three days, then DEFINATELY go. As I have said before on this forum, Istanbul is an amazing city, a perfect syntheses of east and west.