Is that 10 days on the ground? So day #1 is the day you arrive in Athens and day #11 is the day you fly back home? Are you counting days or nights? Typically 2 nights in a place equals 1 day due to the time needed to get there and get settled, then to leave there for the next place. No matter how you count it, it's not much time.
You can fly RT from Athens to Santorini. You can fly RT from Athens to Istanbul. You cannot fly directly between Santorini and Istanbul. You need a visa to go to Istanbul, and the currency is Turkish lira, not Euros. You can get the visa online.
If I remember right, you are going in September. What are you interested in seeing in Istanbul? There is so much to see there (check the RS itinerary), it would require some serious cutting to spend only 2 or 3 days there.
We were on a RS week tour of Istanbul in October. We spent an additional 4 weeks in Greece after that. If you really want to see or learn anything, I'd pick 2 places and stick with them.
One of them would be Athens and the other would be someplace that I really wanted to see or be. Three places in 10 days is just too much, I think.
Our 2 nights in Delphi with one day between for the museum and ruins was my favorite thing of the whole trip. It is a 2-3 hour bus trip each way, so the travel time isn't trivial, especially if you count waiting for the bus.
We spent 4 nights on Santorini. It is beautiful, and I guess it depends on what you go there for, but I wasn't all that impressed.