I have visited all the destinations on your itinerary but definitely not on the same trip!
It looks like you have 9 nights for your trip which translates to 8 full days to explore & enjoy some destinations.
I agree with some of the above posters who mentioned that you will be very rushed & will be spending much of your time in trains or planes rather than actually enjoying each destination you want to visit.
Keep in mind that each day that you travel from point A to point B, you will lose at least half of that day (if not more).
Since you only have 8-9 days for your trip, I'd limit my trip to 2 destinations.
You could also visit Italy for the whole 8-9 days ( Florence & Rome with possible day trips), or you could go Greece & visit Athens, Santorini & any other island of your choice.
You may also choose to visit London & Paris.
Keep in mind that London is very expensive. If you are traveling on a "low budget", I'd probably go to Greece or Italy.
When we traveled to Santorini, we stayed at Gabi Apartments, where we had amazing views of the caldera, the sea & the best sunsets!
The apartment was clean, reasonable and conveniently located a few minutes from Fira.
Here is their website for more information: http://www.gaby-apartments.gr/en/
You may want to read about the beaches in Santorini: http://www.visitgreece.gr/en/sea/beaches/santorini_beaches
Enjoy your trip!
EDIT: If you decide to travel to Greece, you can take the Metro from the airport to Athens, or a taxi which has a flat rate of €35 during the day or €50 at night.
The Metro is very convenient & inexpensive: http://www.ametro.gr/files/images/AttikoMetro_Athens_Map_eng_LG.jpg
Check this website for info regarding taking Metro from airport to city: http://www.athensairporttaxi.com/en/busmetro_metro_en.htm
You may take a ferry from Piraeus (port of Athens) to Santorini (more reasonable than flying): http://www.go-ferry.com/greek-ferry-lines.html
Check this website for more info on travel from airport to Piraeus:http://www.athensinfoguide.com/arrival_airportopiraeus.htm