Don't worry if you see a lot of accommodations that don't have availability for May 2024, the 2023 season has just ended and owners haven't yet set their rates for next year. Some have gone on vacation and won't even respond to emails.
There are no unsafe areas on the islands. If you rent a car you can move away from the main towns and find many more accommodation options in quiet places (especially in Naxos which is the largest island in the Cyclades) but the choice depends mainly on your preferences.
The Plaka district in Athens is one of the most convenient for visiting the main sites if you stay only 2 nights. Almost all major sites will be accessible within a few minutes walk
The only area to avoid is Omonia Square where the atmosphere can disappoint an unaccustomed visitor, and where it is preferable not to walk in the small streets at night. I point this out because this is where you will find cheaper hotel rates.
In Athens you will find plenty of Airbnbs but they can generally only be booked with a minimum stay of 2 or 3 nights.
I know a few (I often go to Athens and never to hotels) but they are accommodations mainly with a single bedroom and a possible sofa/bed in the living room. Given that you will only stay there for 2 nights maximum, a hotel would probably be a better option.
I'm sure that other members in this forum will have have plenty of good hotels to recommand to you.
(but if you insist I can give you information about some interesting Airbnb apartments)
any tips on flying from Athens to Santorini? Airline, etc.
The two Greek airlines are Aegean/Olympic and Sky Express. They are the ones that serve the islands. Aegean is regularly ranked among the best European airlines.
And ferries from Santorini to Naxos?
In mid-May you can take a traditional ferry from Blue Star Ferries (usually the Blue Star Delos) or a high-speed catamaran from Seajets. Seajets are a bit faster (and more expensive). I strongly recommend a Blue Star with which the trip (only 2 hours) will be more pleasant and comfortable.
Below is a video of the Blue Star Delos (with arrival in Naxos)