Jessica,
While this Itinerary might be considered "doable" by some, IMHO this is somewhat unrealistic and overly ambitious. You've mentioned nine locations to be visited in a 21 day period, which averages 2.33 days per location with no allowance for travel times (some of which will be considerable!).
My suggestion would be to reduce the number of locations to perhaps five or six. Choosing locations which are somewhat close geographically will reduce travel times to some extent. Could you indicate which destinations are most important for you to see?
Whether to start in Paris and end in Athens or vice versa will depend to some extent on what time of year this trip will be taking place. As mentioned in the previous post, starting in Paris will provide a somewhat easier "culture shock".
If this is your first trip to Europe, I'd highly recommend reading the Guidebook Europe Through The Back Door before you get too far in your planning. That will provide you with a lot of information, including Itinerary planning details.
When planning your Itinerary, keep in mind one of Rick's main travel planning rules: "Assume you will return"!
Congratulations and good luck in your planning!