Kirsten,
I will generally stay up as late as possible - taking only a nap for the nights sleep when I leave. Remember that your flight is night time at your destination. Eat the "dinner" on the plane and take an Ambien before you go over the Atlantic. On goes my Ipod with soothing music and I am out. Wake up for breakfast as you prepare to land and you are good as new until dinnertime in Athens.
Early to bed at your destination that first night, another Ambien to keep you asleep. They are mild enough that you will wake up refreshed and you will have 10 days of being totally adjusted.
And then on the way home, REVERSE IT - because the jet lag is more difficult when you get back - East to West, plus you no longer have the trip to look forward to - it's back to the salt mine.
I will do three nights of Ambien going and coming now. I got this regimine from my well travelled doctor and it makes the whole coming and going more bearable.