to answer QUestions in order:
(1) ITINERARY - No, NOT so good, picking the 2 places most ballyhooed by Cruise Lines and Travel Agents, to trap gullible people. The Cliche Twins of USA greek travel, THE most crowded/costly even in Sept, & why most other people consider Americans uninformed. However, ONE of isles is worth a short stop, and for island #2, we can give you something more authentic, more fun, more memorable. We've answered this inquiry so many times, that we Old Island fans have come up with a do-able alternative for 10 nights (that really means 9 1/2 days) Our Suggestion = SANTORINI - NAXOS or PAROS - ATHENS.
(2) GETTING AROUND - No your logistic don't work, for such a short time, and sequence is backward. With such a cruelly short time, you can't waste a minute, and going in to Athens at beginning AND end wastes many precious hours. Here's the Strategy:
DAY 1 - Try for a Flight nonstop from N America to Athens, because they arrive in mid-morning. Allow 2-hr layover & catch domestic flight to SANTORINI - you'll get there in time on day ONE to explore Fira Town enjoy sunset dinner - a half-day saved!
DAY 2 - Early am, bus/taxi to OIA to enjoy & take pix before tour crowds jampack the village - then scram to explore elsewhere
DAY 3 - either take 10:30 ChampionJet or 3:15pm BLUE STAR open-deck ferries to next Island (naxos is just 2 hrs)
DAY 4-5-6-7 - Enjoy NAXOS (my choice)or PAROS.. Naxos has vineyards & Fall wine festivals .. 15 miles of golden sand beaches, wonderful rooms w seaview balconies @a fraction of Santorini rates, fascinating port-town lively in Sept. Late on Day 7, either fly back to ATH (40 minutes) or take Blue Star ferry (6pm - 11:45). your choice.
DAY 8-9-10 - Intense Athens Exploring; we have info about D-I-Y Sightseeing &what tours are worth €€.
-- ANCIENT MOTTO for such short trips: If you can't spend the time, you must spend the money... i.e. flights.
OTHER QUESTIONS -- you've asked for too much info in one heap... it would take HOURS to provide thoughtful answers, and that would make us Travel Agents, which we are not. As quick incomplete answers, to follow up, IF you take the advice above:
ATHENS -- 2.5 days is barely enoug but you can do it if up early and have A Plan
MYKONOS - This place is Famous for Being Famous... and I'm not speaking from prejudice, its' just from modern experience (I have been there 3 time, 2x as a lilnk to elsehere). Incredibly expensive, lots of Eurotrash,nightlife mainly in late summer, after 12 or 1 am. Only history involves Delos island, and I'm not sensing you are an Ancient Civ Scholar.
PLACES to STAY - I have specific areas to Recommend, in Santorini, Naxos, Athens. As for AirBnb, have heard some bad stuff lately about people unable to change/get refunds due to disruptions. At least for Athens, booking.com now has pvt apts/room offered, as well as hotels, for very good rates.. and they have the security of refunds/rules. In these uncertain times, COVID-19 still a concern in Europe, I'd play it safer. Booking.com's "see on map" feature can show you availabllity/rates AND exact location of MANY good small hotels & pensions in Santorini & Naxos, Paros, Anti-paros.
DONT-MISS LIST - With all the other "asks" this is one I'd suggest you & spouse defer to another posting
INFORMATIVE VIDEOS -
NAXOS TOUR around ISLE: http://www.flickr.com/photos/stanbr54/sets/72157634605629689/
NAXOS Sept 19 - https://www.flickr.com/photos/stanbr54/albums/72157711294807761
SANTORINI (various) - https://www.flickr.com/photos/stanbr54/sets/72157632154800782/
Why NOT to try Santorini Sunset in Village of OIA - http://tinyurl.com/lnquk6h
WHY ATHENS is WORTH 3 Days - https://www.flickr.com/photos/stanbr54/sets/72157632121475515/
You can put together a good trip if you get busy -- Good luck!