Start off at my favorite hotel in Athens then to 3 different islands in 9 days total.
I highly recommend booking any ATV or Car rentals or boat trips WAY in advance if you're traveling from June - September, things book up very fast.
This itinerary is great for someone who wants to see a lot in a short amount of time - you are moving every 2-3 days.
You can't fly to/from Ios, ferries only. Use the Ferry Hopper app to check the best ferry schedules. I would recommend if you cant find Zante Ferry's on the ferry hopper app then to check their website directly.
Sometimes they release schedules on a wonky time period. You could even flip this around and do Mykonos Milos Ios if the ferrys dont line up correctly to do it the way I suggested in the itinerary.
Fly home on Day 10!