I gather that you have not locked in any accommodations or domestic transport -- Good! Because IMHO, you are doing it backwards. Maybe you have traveled elsewhere in Europe in the Fall (Spain, Italy) where far-flung areas are still lively in October -- NOT the case in Greece. The smaller islands begin rolling up the sidewalks in mid-september... many people from those isles actually live on mainland or larger places (lilke Crete) and are getting their kids back in school etc. So you might find a lot of shuttered shops and very hushed evenings... and hotel & restaurant owners who are friendly but mentally already onward to their own lives.
You can minimize this by a modified reversal -- the first 4 in your list are likeliest to be livelier later. Thus: fly to MILOS... if you like swims and sailboat rides, do 3 days not 2. There's a daily AM fast-ferry to FOLEGANDROS (small cat, but it's only a 55-minute ride). This island's main charm is its "CHORA" (High town) where u should stay 2 nights, then on to SANTORINI. I say (from experience of many visits) that 3 full days (3 nights?) on Santorini is plenty, if you stay on the move. There are several daily ferries to NAXOS; choose one that has outside deck to stand on for the departure view. NAXOS has large permanent population, so the port town is always lively; stay right next to it, on St. George Beach, u can walk to evening activities & the good bus network that serves the whole island. Rent a car at least 1 day to experience all the interests on your list -- PS, it has many vineyards, and in Fall, some village wine festivals. Allot at LEAST 4 days, 5 is better. On to Mykonos for another 2 days. That's 15 days: Decision time!
Yes, Rhodes could fit in now... To get there you could take a ferry (to Rafina OR to Piraeus -- time is roughly the same from 3.5-5 hrs depending on what kind of ferry). Then you'd do local transport to airport (from Piraeaus there's now a handy hourly TRAIN, 60 minutes; Rafina, local bus about 45). You should be able to get a "promotional price" of airfare, if you pick he right day -- less than a ferry ride, and takes 50 mins vs ?15? hours. Rhodes has large permanent population and its Old Town always lively due to cruise line visits late into fall (but stay at far end, away from port -- Look at cute & budget Medieval Inn) ... Lindos bay is a "suntrap" so October is fine for swims ... rent a car & explore rest of island; maybe 5 days. Again, Rhodes represents all the interests on your list! Lucky you to have the time to explore them!
To return to Athens, you could fly (50 minutes), or try an overnighter on a modern large Blue Star ferry (1500 passenger capacity = like a small liner) -- board at 1700-1800 (5-6pm) arrive 8 AM. Single cabin costs a bit, but remember it's travel PLUS hotel - you also can book a berth in an all male cabin for 2 or 4 (that time of year, the other bunk/s may be vacant).
Counting a day for Mykonos-Rhodes travel, that brings you to 21, so you can judge how long to stay in Athens. You may want to give it 5+ days, and then do an overnight to Delphi ... drive or KTEL bus up in late aftenoon, enjoy mountain sunset and views (at my room at back of budget Hotel Pan, hawks circled BELOW my balcony... and the sea gleamed in the distance). Going to site at 8 AM, you can see it before bus tour groups, arrive, check the GOOD museum, then via bus or car, return to ATH or ATH airport ... an inspiring end to a glorious trip of 27-28 days. PS: we are all green with envy!