Go direct from Athens airport to Santorini by plane. Stay on Santorini until you get bored. Then you take a ferry to Mykonos. Save the last 2-3 days for Athens. September is low season and no need for pre-booking ferries. When you buy the ferry ticket from Santorini, the travel agency may help you reserve accomodation on Mykonos. Santorini and Mykonos are not cities, but islands.
Ferry schedules on www.gtp.gr
You have a plan which is as good as any other plan. It is often recommended to be at the main-land the last night(s) before travelling home. In case anything unexpected should happen (strikes, weather etc) you then already are close to the airport for you homebound journey.
When it comes to ferries, I recommend the Blue Star Naxos for the the trip from Pireus (Athens) to Mykonos. It is a large, modern and comfortable ship calling in at Syros and Tinos on its sailing to Mykonos. It is like a small cruise. On the trip from Mykonos to Santorini I would say Flying Cat IV is better than Superjet.
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